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Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : M2D [1]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

The maximum height attained by a projectile and its horizontal range are equal to each other if the projectile is projected at an angle given by :

tan 1 2

(A)

tan

(C) 2.

1

4

(B) (D)

tan 1 3 tan

1

1

(A) (C)

to the bullet, at what height above the target

10 cm 50 cm

(B) (D)

2

8.

(B)

2s

(C)

3s

(D)

3s

A bomb is dropped from an aeroplane when it is at a height h directly above a target. If the aeroplane is moving horizontally at a speed v, the distance by which the bomb will miss the target is given by : (A)

2v

(C)

v

h g

(B)

v

h g

2h g

(D)

v

h 2g

VMC/Motion in Two Dimension

(B)

45

(C)

60

(D)

75

In Q.6, at what minimum altitude should the enemy plane

12.5 km 14.5 km

(B) (D)

13.5 km 15.5 km

The ceiling of a tunnel is 5 m high. What is the maximum horizontal distance that a ball thrown with a speed of 20 ms 1 , can go without hitting the ceiling of the tunnel ? (Take g 10 ms 2 )

A ball is projected horizontally with a velocity of 5ms 1

2s

30

(A) (C)

inclined to each other at an angle of 45 perpendicular to each other

(A)

(A)

fly to avoid being hit ? (Take g 10 ms 2 )

20 cm 100 cm

from the top of a building 19.6 m high. How long will the ball take to hit the ground ?

5.

7.

)

When a projectile is at the highest point of its trajectory, the directions of its velocity and acceleration are : (A) parallel to each other (B) anti-parallel to each other (C) (D)

4.

of 600 ms 1 . At what angle with the vertical should the gun be fired so as to hit the plane ?

5

must he aim his gun in order to hit it? (Take g 10 ms

An enemy plane is flying horizontally at an altitude of 2 km with a speed of 300 ms 1 . An army man with an antiaircraft gun on the ground sights the enemy plane when it is directly overhead and fires a shell with a muzzle speed

A person aims a gun at target located at a horizontal distance of 100 m. If the gun imparts a horizontal speed of

500 ms

3.

6.

9.

(A)

10 3 m

(B)

20 3 m

(C)

30 3 m

(D)

40 3 m

From the top of a tower of height 40 m, a ball is projected upward with a speed of 20 m/s at an angle of elevation of

30 . The ratio of the total time taken by the ball to hit the ground to its time of flight (time taken to come back to the same elevation) is : (Take = 10 m/s2) (A) 2:1 (B) 3:1 (C) 3:2 (D) 1.5 : 1 10.

43

In Q.9, the horizontal displacement (from the foot of the tower) of the ball is approximately equal to : (A) 50 m (B) 60 m (C) 70 m (D) 80 m

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : M2D [2]

ROLL NO.

START TIME :

STUDENT’S SIGNATURE :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

A cannon on a level plain is aimed at an angle above the horizontal and a shell is fired with a muzzle velocity v0 towards a vertical cliff a distance R away. Then the height from the bottom at which the shell strikes the side walls of the cliff is : R sin

1 gR 2 v02 sin 2

(B)

R cos

1 gR 2 2 v02 cos 2

(C)

R tan

1 gR 2 2 v02 cos 2

(D)

1 gR 2 R tan 2 v02 sin 2

It is possible to project a particle with a given velocity in two possible ways so as to make it pass through a point P at a distance r from the point of projection. The product of the times taken to reach this point in the two possible ways is then proportional to : (A) 1/r (B) r

3.

r3

(D)

horizontal. If g 10 ms 1 , after how long will the ball hit the ground ? (A) 1s (C) 3s

7.

Which of the following remains constant during the motion of a projectile fired from a planer ? (A) kinetic energy (B) momentum (C) vertical component of velocity (D) horizontal component of velocity

8.

The horizontal distance x and the vertical height y of a projectile at a time t are given by x = at and y = bt 2 + ct where a, b and c are constant. What is the magnitude of the velocity of the projectile 1 second after it is fired ? (A) [a2 + (2b + c)2]1/2 (B) [2a2 + (b + c)2]1/2 (C) [2a2 + (2b + c)2]1/2 (D) [a2 + (b + 2c)2]1/2

9.

In Q. 8, the angle with the horizontal at which the projectile is projected is given by :

from the gun when it is fired at an angle of 45 to the horizontal. With what speed should the shell be projected so that it hits the car ? (Take g 10 ms 2 )

(C) 4.

20 ms 1 40 ms

1

(B) (D)

30 ms 1 50 ms

2s 4s

A projectile has a maximum range of 200 m. What is the maximum height attained by it ? (A) 25 m (B) 50 m (C) 75 m (D) 100 m

speed of 10 2 ms 1 . The car is at a distance of 150 m

(A)

(B) (D)

6.

1

r2 A gun kept on a straight horizontal road is used to hit a car traveling on the same road away from the gun at a uniform

From the top of tower of height 40 m, a ball is projected upwards with a speed of 20 ms 1 at an angle of 30 to the

2

(A)

(C)

5.

10.

1

(A)

a tan 1 b

(B)

b tan 1 a

(C)

a tan 1 c

(D)

c tan 1 a

In Q.8, the acceleration due to gravity is given by : (A) 2a (B) 2b (C) 2c (D) ac b

In Q.3 what is the distance of the car from the gun when the shell hits it ? (A) 250 m (B) 500 m (C) 750 m (D) 1000 m

VMC/Motion in Two Dimension

44

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : M2D [3]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

Four projectiles are projected with the same speed at angles 20 , 35 , 60 and 75 with the horizontal. The range will be the longest for the projectile whose angle of projection is : (A)

2.

20

(B)

35

60

(C)

(D)

75

A projectile thrown at an angle of 30 with the horizontal has a range R1 and attains a maximum height h1. Another projectile thrown, with the same velocity, at an angle 30 with the vertical, has a range R2 and attains a maximum height h2. The relation between R1 and R2 is : R R1 2 (A) (B) R1 = R2 (C) R1 = 2R2 (D) R1 = 4R2 2

3.

In Q. 2, what is the relation between h1 and h2 ? h h h1 2 h1 2 (A) (B) 4 3

h1

(C)

h2 2

(D)

h1 = h2

4.

The maximum height attained by a projectile is increased by 10% by increasing its speed of projection, without changing the angle of projection. The percentage increase in the horizontal range will be : (A) 20% (B) 15% (C) 10% (D) 5%

5.

A projectile attains a certain maximum height when projected from earth. If it is projected at the same angle and with the same initial speed from the moon, where the acceleration due to gravity is one-sixth that on earth, by what factor will the maximum height of the projectile increase ? (A)

3

(B)

3

6

(C)

(D)

6

6.

A projectile has a range R and time of flight T. If the range is doubled (by increasing the speed of projection, without changing the angle of projection), the time of flight will become : T T (A) (B) (C) (D) 2T 2T 2 2

7.

A projectile has the same R when the maximum height attained by it is either h1 or h2. Then R, h1 and h2 will be related as : (A)

8.

R h1h2

(B)

R 2 h1h2

R 3 h1h2

(C)

(D)

R 4 h1h2

A body is projected horizontally from a point above the ground. The motion of the body is described by the equations x=2t

and

y = 5 t2

where x and y are the horizontal and vertical displacements (in m) respectively at time t. What is the magnitude of the velocity of the body 0.02 second after it is projected ? (A)

2 ms 1

VMC/Motion in Two Dimension

(B)

2 2 ms 1

3.5 ms 1

(C)

45

(D)

5 ms 1

HWT/Physics

Vidyamandir Classes 9.

A body is projected at time t = 0 from a certain point on a planet’s surface with a certain velocity at a certain angle with the planet’s surface (assumed horizontal). The horizontal and vertical displacements x and y (in meters) respectively vary with time t (in second) as x 10 3 t ; y 10 t t 2

What is the magnitude and direction of the velocity with which the body is projected ?

10.

(A)

20 ms 1 at an angle of 30 with the horizontal

(B)

20 ms 1 at an angle of 60 with the horizontal

(C)

10 ms 1 at an angle of 30 with the horizontal

(D)

10 ms 1 at an angle of 60 with the horizontal

Which one of the following statements is NOT true about the motion of a projectile ? (A) The time of flight of a projectile is proportional to the speed with which it is projected (B) The horizontal range of a projectile is proportional to the square-root of the speed with which it is projected (C) (D)

For a given speed of projection, the angle of projection for maximum range is 45 At maximum height, the acceleration due to gravity is perpendicular to the velocity of the projectile

VMC/Motion in Two Dimension

46

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : M2D [4]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

Displacement (x) of a particle is related to time (t) as :

x at bt 2 ct 3

Where a, b and c are constant of motion. The velocity of the particle when its acceleration is zero is given by : (A)

a

b2 c

(B)

a

b2 2c

a

(C)

b2 3c

(D)

a

b2 4c

2.

A vector A is along the positive z-axis and its vector product with another vector B is zero, then vector B could be : ˆj kˆ ˆi ˆj (A) (B) (C) (D) 7 kˆ 4 ˆi

3.

A river is flowing from west to east at a speed of 5 m/minute. In what direction should a man on the south bank of the river capable of swimming at 10 m/minutes in still water swim to cross the river in the shortest time ? (A) East (B) West (C) South (D) North

4.

In Q. 3 above, in what direction should the man swim so that he crosses the river by swimming the shortest distance ? (A)

5.

North

(B)

60 west of north (C)

30 west of north (D)

30 west of south

A body is thrown vertically up with a velocity u. It passes three points A, B and C in its upward journey with velocities

u u u , and 2 3 4

respectively. The ratio AB AC is : (A)

20 27

(B)

2

(C)

(D)

10 7

1

6.

A body is thrown vertically up with a velocity u. It passes a point at a height h above the ground at time t1 while going up and at time t2 while falling down. Then the relation between u, t1 and t2 is : 2u 2u u u (A) t1 t2 (B) t2 t1 (C) t1 t2 (D) t2 t1 g g g g

7.

In Q. 6 above, the relation between t1, t2 and h is : 2h h (A) t1 t2 (B) t1 t2 g g

8.

9.

t1 t2 2

(C)

2h g

(D)

t1 t2 2

h g

A body dropped from a height H above the ground strikes an inclined plane at height h above the ground. As a result of the impact, the velocity of the body becomes horizontal. The body will take the maximum time to reach the ground if : H H H H h h (A) (B) (C) (D) h h 4 2 2 2 2 A body is dropped from the roof of a multi-storeyed building. It passes the ceiling of the 15th storey at a speed of 20 ms 1 . If the height of each storey is 4 m, the number of storeys in the building is : (Take g 10 ms 2 and neglect air resistance) (A) 20 (B) 25 (C) 30 (D) 35

10.

Two balls A and B are projected from the same location simultaneously. Ball A is projected vertically upwards and ball B at 30 to the vertical. They reach the ground simultaneously. The velocities of projection of A and B are in the ratio : (A)

3 :1

VMC/Motion in Two Dimension

(B)

1: 3

(C)

3:2

47

(D)

2: 3

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : M2D [5]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

(A) 2.

3.

8m

(C)

80 m

(D)

800 m

(C)

4.0 s

(D)

8.0 s

2u sin g

(B)

u sin g

2u g sin

(C)

(D)

u g sin

The equation of motion of projectile is y ax bx 2 where a and b constant of motion. The horizontal range of the projectile is : a b

a 2b

(B)

(C)

a2 2b

(D)

a2 4b

a2 2b

(D)

a2 4b

In Q. 4 above, the greatest height attained by the projectile is : (A)

6.

(B)

A body is projected with a velocity u at an angle with the horizontal. The velocity of the body will become perpendicular to the velocity of projection after a time t given by :

(A) 5.

0.8 m

In Q.1 above, the time of flight of the body is : (A) 0.8 s (B) 1.0 s

(A) 4.

A body is projected with a velocity v 3ˆi 4 ˆj ms 1 . The maximum height attained by the body is : (Take g 10 ms 2 )

a b

a 2b

(B)

(C)

In Q. 4 above, the time of flight of the projectile is : 2 a a (A) (B) bg bg

2a bg

(C)

a 2bg

(D)

7.

A particle moving in a straight line covers half the distance with a speed of 3 m/s. The other half of the distance is covered in two equal time intervals with speeds of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is : (A) 4.0 m/s (B) 5.0 m/s (C) 5.5 m/s (D) 4.8 m/s

8.

A car is traveling at a velocity of 10 km/h on a straight road. The driver of the car throws a road. If the parcel is to reach the man, the direction of throw makes the following angle with the direction of the car, (A)

9.

10.

135

(B)

45

tan 1

(C)

2

(D)

In 1.0 s, a particle goes from point A to point B, moving in a semicircle of radius 1.0 m as shown in the figure. The magnitude of the average velocity of the particle is : (A)

3.14 ms 1

(B)

2.0 ms 1

(C)

1.0 ms 1

(D)

Zero

The initial velocity of a particle is u 4ˆi 3 ˆj ms

1 tan 1 2

A 1.0 m B

1

. It is moving with uniform acceleration a 0.4ˆi 0.3 ˆj ms 2 . The magnitude

of its velocity after 10 s is : (A)

3 ms 1

VMC/Motion in Two Dimension

(B)

4 ms 1

5 ms 1

(C)

48

(D)

10 ms 1

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : M2D [6]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

The horizontal and vertical displacements of a projectile at time ' t' are x 36t and y 48t 4.9 t 2 respectively where x and y are in metre and t is in second. Initial velocity of the projectile in m/s is : (A) 15 (B) 30 (C)

2.

45

(D)

60

The displacement x of a particle moving in one dimension is related to time t by the equation t

x 3

Where x is in metres and t in seconds. The displacement of the particle when its velocity is zero is : (A) zero (B) 4m (C) 1m (D) 0.5 m 3.

A particle initially (i.e., at t = 0) moving with a velocity u is subjected to a retarding force, as a result of which it decelerates at a rate a k v

where v is the instantaneous velocity and k is a positive constant. The time T taken by the particle to come to rest is given by : (A) 4.

T

2 u k

T

(B)

2u k

T

(C)

A particle starts from rest. Its acceleration at time t = 0 is

a

5 ms 2 which varies with time as shown in figure.

2u 3 / 2 k

T

(D)

2u 2 k

5 ms 2

The maximum speed of the particle will be :

5.

(A)

7.5 ms 1

(B)

15 ms 1

(C)

30 ms 1

(D)

7.5 ms 1

O

Figure shows the variation of velocity (v) of a body with position (x) from the origin O. Which of the graphs shown in figure correctly represents the variation of the acceleration (a) with position (x) ?

(A)

(B)

O 6.

(C)

O

x

v v0

a O

x

x0

O

a

a

t

6 sec

x

a O

(D)

x

x

The velocity (v) of a body moving along the positive x-direction varies with displacement (x) from the origin as v k x , where k is a constant. Which of the graphs shown in figure correctly represents the displacement-time x t graph of the motion ?

(A)

O

x

x

x

(B)

t

VMC/Motion in Two Dimension

x

(C)

O

t

(D)

O

49

t

O

t

HWT/Physics

Vidyamandir Classes 7.

A tennis ball rolls off the top of a stair case way with a horizontal velocity u ms 1 . If the steps are b metre wide and h metre high, the ball will hit the edge of the nth step, if : (A)

n

2hu gb

8.

n

(B)

2

gb

n

(C)

2

2hu 2 gb

(A)

hu gb 2

1 tan 1 5

(B)

1 tan 5

tan 1

(C)

tan 1 5

(D)

An aeroplane is flying in a horizontal direction with a velocity 600 kmh 1 at a height

O

of 1960 m. When it is vertically above the point A on the ground, a body is dropped from it. The body strikes the ground at point B. Calculate the distance AB : (A) 3.33 km (B) 333 km (C) 33.3 km (D) 3330 km 10.

n

(D)

A bomber plane moves horizontally with a speed of 500 ms 1 and a bomb released from it, strikes the ground in 10 s. Angle at which it strikes the ground will be : g 10 ms 2

9.

2hu 2

v

h B

A

A particle P is at the origin starts with velocity v 2ˆi 4 ˆj ms 1 with constant acceleration 3ˆi 5 ˆj ms 2 . After traveling for 2 s, its

distance from the origin is : (A) 10 m (B)

VMC/Motion in Two Dimension

20.6 m

(C)

9.8 m

50

(D)

11.7 m

HWT/Physics

Vidyamandir Classes DATE :

IITJEE :

TIME : 25 MINUTES

MARKS : 10

NAME :

TEST CODE : M2D [7]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

A man standing on a hill top projects a stone horizontally with speed v0 as shown in figure. Taking the coordinate system as given in the figure. The coordinates of the point where the stone will hit the hill surface : (A)

2v02 tan 2v02 tan 2 , g g

(C)

2v02 tan g

,

g

2v02

(B)

2v02 2v02 tan 2 , g g

(D)

2v02 tan g

,

y

v0

2v02 tan 2 g

x

(0, 0)

A particle moves in the x-y plane with velocity vx 8t 2 and vy = 2. If it passes through the point x = 14 and y = 4 at t = 2s, find the equation (x-y relation) of the path. (A)

3.

x y2 y 2

(B)

x 2 y2 2 y 3

x = 3y2 + 5

(C)

(D)

can not be found from above data

A particle leaves the origin with an initial velocity v 3.00ˆi ms 1 and a constant acceleration a 1.00 ˆi 0.50 ˆj ms 2 . When the

particles reaches it maximum x-coordinate, what is its y-component a velocity ? (A) 4.

2.0 ms 1

(B)

1.0 ms 1

1.5 ms 1

(C)

(D)

1.0 ms 1

A particle starts from the origin of coordinates at time t = 0 and moves in the x-y plane with a constant acceleration in the y-direction. Its equation of motion is y x 2 . Its velocity component in the x-direction is : (A)

5.

variable

(D)

2

(B)

6s

(C)

7s

(D)

10 s

A glass marble projected horizontally from the top of a table falls at a distance x from the edge of the table. If h is the height of the table, then the velocity of projection is : (A)

7.

2

(C)

An aeroplane flying horizontally with a speed of 360 kmh 1 releases a bomb at a height of 490 m from the ground. When will the bomb strike the ground ? (A) 8s

6.

2

(B)

h

g 2x

(B)

x

g 2h

(C)

gxh

(D)

gx + h

A bomb is dropped on an enemy post by an aeroplane flying horizontally with a velocity of 60 kmh 1 and at a height of 490 m. At the time of dropping the bomb, how far horizontally the aeroplane should be from the enemy post so that the bomb may directly hit the target ? 400 500 1700 m m m (A) (B) (C) (D) 498 m 3 3 3

VMC/Motion in Two Dimension

51

HWT/Physics

Vidyamandir Classes 8.

A monkey can jump a maximum horizontal distance of 20 m. Then the velocity of the monkey is : (A)

9.

(B)

14 ms 1

20 ms 1

(C)

(D)

24 ms 1

A body is projected horizontally with speed 20 ms 1 . The approximate displacement of the body after 5 s is : (A)

10.

10 ms 1

80 m

(B)

120 m

(C)

160 m

(D)

320 m

A body of mass m thrown horizontally with velocity v, from the top of tower of height h touches the level ground at distance of 250 m from the foot of the tower. A body of mass 2 m thrown horizontally with velocity v 2 , from the top of tower of height 4h will touch the level ground at a distance x from the foot of tower. The value of x is : (A)

250 m

VMC/Motion in Two Dimension

(B)

500 m

(C)

125 m

52

(D)

250 2 m

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : M2D [8]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

Two tall buildings are 40 m apart. With what speed must a ball be thrown horizontally from a window 145 m above the ground in one building, so that it will enter a window 22.5 m from the ground in the other ?

5 ms 1

(A) 2.

(B)

8 ms 1

10 ms 1

(C)

(D)

16 ms 1

Two projectile are thrown with the same initial velocity at angles and 90 with the horizontal. The maximum heights attained by them are h1 and h2 respectively. Then h1 h2 is equal to :

sin 2

(A)

(B)

cos 2

tan 2

(C)

(D)

1

3.

When a projectile is projected at a certain angle with the horizontal, its horizontal range is R and time of flight is T1. When the same projectile is throwing with the same speed at some other angle with the horizontal, its horizontal range is R and time of flight is T2. The product of T1 and T2 is : R 2R 3R 4R (A) (B) (C) (D) g g g g

4.

A stone is thrown with a velocity v making an angle with the horizontal. At some instant, its velocity V is perpendicular to the initial velocity v. Then V is : (A) (B) (C) (D) v sin v cos v tan v cot

5.

The equation of a projectile is y 3 x

tan

(A) 6.

1 3

(B)

gx 2 . The angle of projection is given by : 2 (C) tan 3 2

(D)

zero

A projectile of mass m is thrown with a velocity v making an angle of 45 with the horizontal. The change in momentum from departure to arrival along vertical direction, is : mv (A) 2 mv (B) (C) mv (D) 2 mv 2

Paragraph for Q.7 - 10 A stone is projected horizontally off a cliff with velocity 10 m/s. It lands at a distance 'd ' from the foot of the cliff after 6 second. Take g = 10 m/s2

u 10 ms 1

B h

Cliff d

7.

The height of the cliff is___. (A) 60 m (B)

VMC/Motion in Two Dimension

120 m

(C)

180 m

53

(D)

240 m

HWT/Physics

Vidyamandir Classes 8.

9.

10.

The distance 'd ' is_____. (A) 60 m

(B)

45 m

(C)

30 m

The velocity of the stone at the time of impact with the ground is_____. (A) 10 m/s (B) 70 m/s (C) 60.8 m/s

(D)

15 m

(D)

70.2 m/s

(D)

3 s 2

The stone is moving with double its initial speed at time______. (A)

2s

VMC/Motion in Two Dimension

(B)

1s

(C)

3s

54

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : M2D [9]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

A projectile shot into air at some angle with the horizontal has a range of 200 m. If the time of flight is 5 s, then the horizontal component of the velocity of the projectile at the highest point of trajectory is : (A)

40 ms 1

(C)

9.8 ms 1

4.

5.

(D)

Equal to the velocity of projection of the projectile

If the angle of projection of a projectile is 30 , then how many times the horizontal range is larger than the maximum height ? 2

(B)

3

(C)

3 4

(D)

4 3

A particle is projected from the ground with an initial speed of v at an angle with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is : v v v 1 2 cos 2 1 cos 2 1 3 cos 2 (A) (B) (C) (D) v cos 2 2 2 3 The equation of motion of a projectile is y 12 x x 2 . The horizontal component of velocity is 3ms 1 . What is the range of the 4 projectile ? (A) 18 m (B) 16 m (C) 12 m (D) 21.6 m

v-t graph for a projectile, where v is vertical component of velocity, is____.

v

v

(A)

v

(B)

v

(C)

t 6.

0 ms 1

(A) 3.

(B)

(D)

t

t

Range of a projectile with time of flight 10 s and maximum height 100 m is : (g = 10 m/s2) (A) 200 m (B) 125 m (C) 100 m (D)

t

Data incorrect

Paragraph for Q.7 - 10 A ball is thrown upwards from the top of an incline with angle of projection with the vertical. If 60 , and g = 10 m/s2.

u 10 m / s

30m

7.

The time of flight is______. (A) (B) t 3s

VMC/Motion in Two Dimension

t4s

t 3s

(C)

55

(D)

t6s

HWT/Physics

Vidyamandir Classes 8.

The angle if the ball lands exactly at the foot of the incline is____. (A)

9.

(B)

tan 1 6

tan 1

(C)

3/2

(D)

tan 1 2 3

A ball moves in a circular slot with angular acceleration 2 rad / s 2 , the angle between its velocity and acceleration is_____. (A)

10.

tan 1 3

90

(B)

tan 1 (2t ) 2

t tan 1 2

(C)

(D)

45

A particle moves along a parabolic path y = ax2 such that x component of the velocity is constant, say c. The acceleration of this particle is_____. 2ac 2 ˆj ac 2 ˆj (A) (B) (C) 2ac 2 kˆ (D) ac kˆ

VMC/Motion in Two Dimension

56

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : M2D [10]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A particle is projected from a point A with velocity u 2 an angle of 45 with horizontal as shown in figure. It strikes the plane BC at right angles. The velocity of the particle at the time of collision is : (A) (C)

2.

(B)

u 2

(D)

u

u 2

60

45

A

B

An airplane, diving at an angle of 53.0 with the vertical releases a projectile at an altitude of 730 m. The projectile hits the ground 5.00 s after being released. What is the speed of the aircraft ? (A)

3.

3u 2 2u 3

C

282 ms 1

202 ms 1

(B)

182 ms 1

(C)

(D)

102 ms 1

A particle A is projected from the ground with an initial velocity of 10 ms 1 at an angle of 60 with horizontal. From what height h should an another particle B be projected horizontally with velocity 5 ms 1 so that both the particle collide in ground at point C if both

are projected simultaneously ? g 10 ms 2

B

5ms 1 10 ms 1

h 60

A (A) 4.

C

10 m

(B)

30 m

(C)

15 m

A very broad elevator is going up vertically with a constant acceleration of 2 ms

(D) 2

25 m

. At the instant when its velocity is 4 ms 1 a ball is

projected from the floor of the list with a speed of 4 ms 1 relative to the floor at an elevation of 30 . The time taken by the ball to return

the floor is : g 10 ms 2 (A) 5.

1/2 s

(B)

1/3 s

(C)

1/4 s

(A)

10.6 m

(B)

12.8 m

(C)

15.4 m

(D)

24.2 m

(C)

45

(D)

45

(D)

2g R 3

Range is maximum for angle of projection : (A)

7.

1s

A particle is projected from the ground at an angle of 60 with horizontal with speed u 20 ms 1 . The radius of curvature of the path of the particle, when its velocity makes an angle of 30 with horizontal is : g 10 ms 2

6.

(D)

30 60

(B)

45

For a fixed range of projectile, 'R', the minimum velocity of projection is______. (A)

gR

VMC/Motion in Two Dimension

(B)

2 gR

2g R

(C)

57

HWT/Physics

Vidyamandir Classes 8.

A man in a moving bus drops a bag from a height 2 m. The bag lands on the ground with a velocity 10 m/s. The velocity of the bus at the moment he dropped the bag was_____. (A)

9.

10.

10 m/s

(B)

2 10 m / s

The time it takes the bag to reach the ground is_____. 1 2 (A) (B) s s 5 5

(C)

2 15 m / s

2 s 5

(C)

(D)

5 m/s

(D)

2 5s

A boy throws a ball upwards with velocity v at an angle with the horizontal and immediately starts running. How fast must he run to catch the ball ? (A) (B) (C) (D) v/2 v cos v sin v tan

VMC/Motion in Two Dimension

58

HWT/Physics

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DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : M2D [1]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

The maximum height attained by a projectile and its horizontal range are equal to each other if the projectile is projected at an angle given by :

tan 1 2

(A)

tan

(C) 2.

1

4

(B) (D)

tan 1 3 tan

1

1

(A) (C)

to the bullet, at what height above the target

10 cm 50 cm

(B) (D)

2

8.

(B)

2s

(C)

3s

(D)

3s

A bomb is dropped from an aeroplane when it is at a height h directly above a target. If the aeroplane is moving horizontally at a speed v, the distance by which the bomb will miss the target is given by : (A)

2v

(C)

v

h g

(B)

v

h g

2h g

(D)

v

h 2g

VMC/Motion in Two Dimension

(B)

45

(C)

60

(D)

75

In Q.6, at what minimum altitude should the enemy plane

12.5 km 14.5 km

(B) (D)

13.5 km 15.5 km

The ceiling of a tunnel is 5 m high. What is the maximum horizontal distance that a ball thrown with a speed of 20 ms 1 , can go without hitting the ceiling of the tunnel ? (Take g 10 ms 2 )

A ball is projected horizontally with a velocity of 5ms 1

2s

30

(A) (C)

inclined to each other at an angle of 45 perpendicular to each other

(A)

(A)

fly to avoid being hit ? (Take g 10 ms 2 )

20 cm 100 cm

from the top of a building 19.6 m high. How long will the ball take to hit the ground ?

5.

7.

)

When a projectile is at the highest point of its trajectory, the directions of its velocity and acceleration are : (A) parallel to each other (B) anti-parallel to each other (C) (D)

4.

of 600 ms 1 . At what angle with the vertical should the gun be fired so as to hit the plane ?

5

must he aim his gun in order to hit it? (Take g 10 ms

An enemy plane is flying horizontally at an altitude of 2 km with a speed of 300 ms 1 . An army man with an antiaircraft gun on the ground sights the enemy plane when it is directly overhead and fires a shell with a muzzle speed

A person aims a gun at target located at a horizontal distance of 100 m. If the gun imparts a horizontal speed of

500 ms

3.

6.

9.

(A)

10 3 m

(B)

20 3 m

(C)

30 3 m

(D)

40 3 m

From the top of a tower of height 40 m, a ball is projected upward with a speed of 20 m/s at an angle of elevation of

30 . The ratio of the total time taken by the ball to hit the ground to its time of flight (time taken to come back to the same elevation) is : (Take = 10 m/s2) (A) 2:1 (B) 3:1 (C) 3:2 (D) 1.5 : 1 10.

43

In Q.9, the horizontal displacement (from the foot of the tower) of the ball is approximately equal to : (A) 50 m (B) 60 m (C) 70 m (D) 80 m

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : M2D [2]

ROLL NO.

START TIME :

STUDENT’S SIGNATURE :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

A cannon on a level plain is aimed at an angle above the horizontal and a shell is fired with a muzzle velocity v0 towards a vertical cliff a distance R away. Then the height from the bottom at which the shell strikes the side walls of the cliff is : R sin

1 gR 2 v02 sin 2

(B)

R cos

1 gR 2 2 v02 cos 2

(C)

R tan

1 gR 2 2 v02 cos 2

(D)

1 gR 2 R tan 2 v02 sin 2

It is possible to project a particle with a given velocity in two possible ways so as to make it pass through a point P at a distance r from the point of projection. The product of the times taken to reach this point in the two possible ways is then proportional to : (A) 1/r (B) r

3.

r3

(D)

horizontal. If g 10 ms 1 , after how long will the ball hit the ground ? (A) 1s (C) 3s

7.

Which of the following remains constant during the motion of a projectile fired from a planer ? (A) kinetic energy (B) momentum (C) vertical component of velocity (D) horizontal component of velocity

8.

The horizontal distance x and the vertical height y of a projectile at a time t are given by x = at and y = bt 2 + ct where a, b and c are constant. What is the magnitude of the velocity of the projectile 1 second after it is fired ? (A) [a2 + (2b + c)2]1/2 (B) [2a2 + (b + c)2]1/2 (C) [2a2 + (2b + c)2]1/2 (D) [a2 + (b + 2c)2]1/2

9.

In Q. 8, the angle with the horizontal at which the projectile is projected is given by :

from the gun when it is fired at an angle of 45 to the horizontal. With what speed should the shell be projected so that it hits the car ? (Take g 10 ms 2 )

(C) 4.

20 ms 1 40 ms

1

(B) (D)

30 ms 1 50 ms

2s 4s

A projectile has a maximum range of 200 m. What is the maximum height attained by it ? (A) 25 m (B) 50 m (C) 75 m (D) 100 m

speed of 10 2 ms 1 . The car is at a distance of 150 m

(A)

(B) (D)

6.

1

r2 A gun kept on a straight horizontal road is used to hit a car traveling on the same road away from the gun at a uniform

From the top of tower of height 40 m, a ball is projected upwards with a speed of 20 ms 1 at an angle of 30 to the

2

(A)

(C)

5.

10.

1

(A)

a tan 1 b

(B)

b tan 1 a

(C)

a tan 1 c

(D)

c tan 1 a

In Q.8, the acceleration due to gravity is given by : (A) 2a (B) 2b (C) 2c (D) ac b

In Q.3 what is the distance of the car from the gun when the shell hits it ? (A) 250 m (B) 500 m (C) 750 m (D) 1000 m

VMC/Motion in Two Dimension

44

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : M2D [3]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

Four projectiles are projected with the same speed at angles 20 , 35 , 60 and 75 with the horizontal. The range will be the longest for the projectile whose angle of projection is : (A)

2.

20

(B)

35

60

(C)

(D)

75

A projectile thrown at an angle of 30 with the horizontal has a range R1 and attains a maximum height h1. Another projectile thrown, with the same velocity, at an angle 30 with the vertical, has a range R2 and attains a maximum height h2. The relation between R1 and R2 is : R R1 2 (A) (B) R1 = R2 (C) R1 = 2R2 (D) R1 = 4R2 2

3.

In Q. 2, what is the relation between h1 and h2 ? h h h1 2 h1 2 (A) (B) 4 3

h1

(C)

h2 2

(D)

h1 = h2

4.

The maximum height attained by a projectile is increased by 10% by increasing its speed of projection, without changing the angle of projection. The percentage increase in the horizontal range will be : (A) 20% (B) 15% (C) 10% (D) 5%

5.

A projectile attains a certain maximum height when projected from earth. If it is projected at the same angle and with the same initial speed from the moon, where the acceleration due to gravity is one-sixth that on earth, by what factor will the maximum height of the projectile increase ? (A)

3

(B)

3

6

(C)

(D)

6

6.

A projectile has a range R and time of flight T. If the range is doubled (by increasing the speed of projection, without changing the angle of projection), the time of flight will become : T T (A) (B) (C) (D) 2T 2T 2 2

7.

A projectile has the same R when the maximum height attained by it is either h1 or h2. Then R, h1 and h2 will be related as : (A)

8.

R h1h2

(B)

R 2 h1h2

R 3 h1h2

(C)

(D)

R 4 h1h2

A body is projected horizontally from a point above the ground. The motion of the body is described by the equations x=2t

and

y = 5 t2

where x and y are the horizontal and vertical displacements (in m) respectively at time t. What is the magnitude of the velocity of the body 0.02 second after it is projected ? (A)

2 ms 1

VMC/Motion in Two Dimension

(B)

2 2 ms 1

3.5 ms 1

(C)

45

(D)

5 ms 1

HWT/Physics

Vidyamandir Classes 9.

A body is projected at time t = 0 from a certain point on a planet’s surface with a certain velocity at a certain angle with the planet’s surface (assumed horizontal). The horizontal and vertical displacements x and y (in meters) respectively vary with time t (in second) as x 10 3 t ; y 10 t t 2

What is the magnitude and direction of the velocity with which the body is projected ?

10.

(A)

20 ms 1 at an angle of 30 with the horizontal

(B)

20 ms 1 at an angle of 60 with the horizontal

(C)

10 ms 1 at an angle of 30 with the horizontal

(D)

10 ms 1 at an angle of 60 with the horizontal

Which one of the following statements is NOT true about the motion of a projectile ? (A) The time of flight of a projectile is proportional to the speed with which it is projected (B) The horizontal range of a projectile is proportional to the square-root of the speed with which it is projected (C) (D)

For a given speed of projection, the angle of projection for maximum range is 45 At maximum height, the acceleration due to gravity is perpendicular to the velocity of the projectile

VMC/Motion in Two Dimension

46

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : M2D [4]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

Displacement (x) of a particle is related to time (t) as :

x at bt 2 ct 3

Where a, b and c are constant of motion. The velocity of the particle when its acceleration is zero is given by : (A)

a

b2 c

(B)

a

b2 2c

a

(C)

b2 3c

(D)

a

b2 4c

2.

A vector A is along the positive z-axis and its vector product with another vector B is zero, then vector B could be : ˆj kˆ ˆi ˆj (A) (B) (C) (D) 7 kˆ 4 ˆi

3.

A river is flowing from west to east at a speed of 5 m/minute. In what direction should a man on the south bank of the river capable of swimming at 10 m/minutes in still water swim to cross the river in the shortest time ? (A) East (B) West (C) South (D) North

4.

In Q. 3 above, in what direction should the man swim so that he crosses the river by swimming the shortest distance ? (A)

5.

North

(B)

60 west of north (C)

30 west of north (D)

30 west of south

A body is thrown vertically up with a velocity u. It passes three points A, B and C in its upward journey with velocities

u u u , and 2 3 4

respectively. The ratio AB AC is : (A)

20 27

(B)

2

(C)

(D)

10 7

1

6.

A body is thrown vertically up with a velocity u. It passes a point at a height h above the ground at time t1 while going up and at time t2 while falling down. Then the relation between u, t1 and t2 is : 2u 2u u u (A) t1 t2 (B) t2 t1 (C) t1 t2 (D) t2 t1 g g g g

7.

In Q. 6 above, the relation between t1, t2 and h is : 2h h (A) t1 t2 (B) t1 t2 g g

8.

9.

t1 t2 2

(C)

2h g

(D)

t1 t2 2

h g

A body dropped from a height H above the ground strikes an inclined plane at height h above the ground. As a result of the impact, the velocity of the body becomes horizontal. The body will take the maximum time to reach the ground if : H H H H h h (A) (B) (C) (D) h h 4 2 2 2 2 A body is dropped from the roof of a multi-storeyed building. It passes the ceiling of the 15th storey at a speed of 20 ms 1 . If the height of each storey is 4 m, the number of storeys in the building is : (Take g 10 ms 2 and neglect air resistance) (A) 20 (B) 25 (C) 30 (D) 35

10.

Two balls A and B are projected from the same location simultaneously. Ball A is projected vertically upwards and ball B at 30 to the vertical. They reach the ground simultaneously. The velocities of projection of A and B are in the ratio : (A)

3 :1

VMC/Motion in Two Dimension

(B)

1: 3

(C)

3:2

47

(D)

2: 3

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : M2D [5]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

(A) 2.

3.

8m

(C)

80 m

(D)

800 m

(C)

4.0 s

(D)

8.0 s

2u sin g

(B)

u sin g

2u g sin

(C)

(D)

u g sin

The equation of motion of projectile is y ax bx 2 where a and b constant of motion. The horizontal range of the projectile is : a b

a 2b

(B)

(C)

a2 2b

(D)

a2 4b

a2 2b

(D)

a2 4b

In Q. 4 above, the greatest height attained by the projectile is : (A)

6.

(B)

A body is projected with a velocity u at an angle with the horizontal. The velocity of the body will become perpendicular to the velocity of projection after a time t given by :

(A) 5.

0.8 m

In Q.1 above, the time of flight of the body is : (A) 0.8 s (B) 1.0 s

(A) 4.

A body is projected with a velocity v 3ˆi 4 ˆj ms 1 . The maximum height attained by the body is : (Take g 10 ms 2 )

a b

a 2b

(B)

(C)

In Q. 4 above, the time of flight of the projectile is : 2 a a (A) (B) bg bg

2a bg

(C)

a 2bg

(D)

7.

A particle moving in a straight line covers half the distance with a speed of 3 m/s. The other half of the distance is covered in two equal time intervals with speeds of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is : (A) 4.0 m/s (B) 5.0 m/s (C) 5.5 m/s (D) 4.8 m/s

8.

A car is traveling at a velocity of 10 km/h on a straight road. The driver of the car throws a road. If the parcel is to reach the man, the direction of throw makes the following angle with the direction of the car, (A)

9.

10.

135

(B)

45

tan 1

(C)

2

(D)

In 1.0 s, a particle goes from point A to point B, moving in a semicircle of radius 1.0 m as shown in the figure. The magnitude of the average velocity of the particle is : (A)

3.14 ms 1

(B)

2.0 ms 1

(C)

1.0 ms 1

(D)

Zero

The initial velocity of a particle is u 4ˆi 3 ˆj ms

1 tan 1 2

A 1.0 m B

1

. It is moving with uniform acceleration a 0.4ˆi 0.3 ˆj ms 2 . The magnitude

of its velocity after 10 s is : (A)

3 ms 1

VMC/Motion in Two Dimension

(B)

4 ms 1

5 ms 1

(C)

48

(D)

10 ms 1

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : M2D [6]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

The horizontal and vertical displacements of a projectile at time ' t' are x 36t and y 48t 4.9 t 2 respectively where x and y are in metre and t is in second. Initial velocity of the projectile in m/s is : (A) 15 (B) 30 (C)

2.

45

(D)

60

The displacement x of a particle moving in one dimension is related to time t by the equation t

x 3

Where x is in metres and t in seconds. The displacement of the particle when its velocity is zero is : (A) zero (B) 4m (C) 1m (D) 0.5 m 3.

A particle initially (i.e., at t = 0) moving with a velocity u is subjected to a retarding force, as a result of which it decelerates at a rate a k v

where v is the instantaneous velocity and k is a positive constant. The time T taken by the particle to come to rest is given by : (A) 4.

T

2 u k

T

(B)

2u k

T

(C)

A particle starts from rest. Its acceleration at time t = 0 is

a

5 ms 2 which varies with time as shown in figure.

2u 3 / 2 k

T

(D)

2u 2 k

5 ms 2

The maximum speed of the particle will be :

5.

(A)

7.5 ms 1

(B)

15 ms 1

(C)

30 ms 1

(D)

7.5 ms 1

O

Figure shows the variation of velocity (v) of a body with position (x) from the origin O. Which of the graphs shown in figure correctly represents the variation of the acceleration (a) with position (x) ?

(A)

(B)

O 6.

(C)

O

x

v v0

a O

x

x0

O

a

a

t

6 sec

x

a O

(D)

x

x

The velocity (v) of a body moving along the positive x-direction varies with displacement (x) from the origin as v k x , where k is a constant. Which of the graphs shown in figure correctly represents the displacement-time x t graph of the motion ?

(A)

O

x

x

x

(B)

t

VMC/Motion in Two Dimension

x

(C)

O

t

(D)

O

49

t

O

t

HWT/Physics

Vidyamandir Classes 7.

A tennis ball rolls off the top of a stair case way with a horizontal velocity u ms 1 . If the steps are b metre wide and h metre high, the ball will hit the edge of the nth step, if : (A)

n

2hu gb

8.

n

(B)

2

gb

n

(C)

2

2hu 2 gb

(A)

hu gb 2

1 tan 1 5

(B)

1 tan 5

tan 1

(C)

tan 1 5

(D)

An aeroplane is flying in a horizontal direction with a velocity 600 kmh 1 at a height

O

of 1960 m. When it is vertically above the point A on the ground, a body is dropped from it. The body strikes the ground at point B. Calculate the distance AB : (A) 3.33 km (B) 333 km (C) 33.3 km (D) 3330 km 10.

n

(D)

A bomber plane moves horizontally with a speed of 500 ms 1 and a bomb released from it, strikes the ground in 10 s. Angle at which it strikes the ground will be : g 10 ms 2

9.

2hu 2

v

h B

A

A particle P is at the origin starts with velocity v 2ˆi 4 ˆj ms 1 with constant acceleration 3ˆi 5 ˆj ms 2 . After traveling for 2 s, its

distance from the origin is : (A) 10 m (B)

VMC/Motion in Two Dimension

20.6 m

(C)

9.8 m

50

(D)

11.7 m

HWT/Physics

Vidyamandir Classes DATE :

IITJEE :

TIME : 25 MINUTES

MARKS : 10

NAME :

TEST CODE : M2D [7]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

A man standing on a hill top projects a stone horizontally with speed v0 as shown in figure. Taking the coordinate system as given in the figure. The coordinates of the point where the stone will hit the hill surface : (A)

2v02 tan 2v02 tan 2 , g g

(C)

2v02 tan g

,

g

2v02

(B)

2v02 2v02 tan 2 , g g

(D)

2v02 tan g

,

y

v0

2v02 tan 2 g

x

(0, 0)

A particle moves in the x-y plane with velocity vx 8t 2 and vy = 2. If it passes through the point x = 14 and y = 4 at t = 2s, find the equation (x-y relation) of the path. (A)

3.

x y2 y 2

(B)

x 2 y2 2 y 3

x = 3y2 + 5

(C)

(D)

can not be found from above data

A particle leaves the origin with an initial velocity v 3.00ˆi ms 1 and a constant acceleration a 1.00 ˆi 0.50 ˆj ms 2 . When the

particles reaches it maximum x-coordinate, what is its y-component a velocity ? (A) 4.

2.0 ms 1

(B)

1.0 ms 1

1.5 ms 1

(C)

(D)

1.0 ms 1

A particle starts from the origin of coordinates at time t = 0 and moves in the x-y plane with a constant acceleration in the y-direction. Its equation of motion is y x 2 . Its velocity component in the x-direction is : (A)

5.

variable

(D)

2

(B)

6s

(C)

7s

(D)

10 s

A glass marble projected horizontally from the top of a table falls at a distance x from the edge of the table. If h is the height of the table, then the velocity of projection is : (A)

7.

2

(C)

An aeroplane flying horizontally with a speed of 360 kmh 1 releases a bomb at a height of 490 m from the ground. When will the bomb strike the ground ? (A) 8s

6.

2

(B)

h

g 2x

(B)

x

g 2h

(C)

gxh

(D)

gx + h

A bomb is dropped on an enemy post by an aeroplane flying horizontally with a velocity of 60 kmh 1 and at a height of 490 m. At the time of dropping the bomb, how far horizontally the aeroplane should be from the enemy post so that the bomb may directly hit the target ? 400 500 1700 m m m (A) (B) (C) (D) 498 m 3 3 3

VMC/Motion in Two Dimension

51

HWT/Physics

Vidyamandir Classes 8.

A monkey can jump a maximum horizontal distance of 20 m. Then the velocity of the monkey is : (A)

9.

(B)

14 ms 1

20 ms 1

(C)

(D)

24 ms 1

A body is projected horizontally with speed 20 ms 1 . The approximate displacement of the body after 5 s is : (A)

10.

10 ms 1

80 m

(B)

120 m

(C)

160 m

(D)

320 m

A body of mass m thrown horizontally with velocity v, from the top of tower of height h touches the level ground at distance of 250 m from the foot of the tower. A body of mass 2 m thrown horizontally with velocity v 2 , from the top of tower of height 4h will touch the level ground at a distance x from the foot of tower. The value of x is : (A)

250 m

VMC/Motion in Two Dimension

(B)

500 m

(C)

125 m

52

(D)

250 2 m

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : M2D [8]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

Two tall buildings are 40 m apart. With what speed must a ball be thrown horizontally from a window 145 m above the ground in one building, so that it will enter a window 22.5 m from the ground in the other ?

5 ms 1

(A) 2.

(B)

8 ms 1

10 ms 1

(C)

(D)

16 ms 1

Two projectile are thrown with the same initial velocity at angles and 90 with the horizontal. The maximum heights attained by them are h1 and h2 respectively. Then h1 h2 is equal to :

sin 2

(A)

(B)

cos 2

tan 2

(C)

(D)

1

3.

When a projectile is projected at a certain angle with the horizontal, its horizontal range is R and time of flight is T1. When the same projectile is throwing with the same speed at some other angle with the horizontal, its horizontal range is R and time of flight is T2. The product of T1 and T2 is : R 2R 3R 4R (A) (B) (C) (D) g g g g

4.

A stone is thrown with a velocity v making an angle with the horizontal. At some instant, its velocity V is perpendicular to the initial velocity v. Then V is : (A) (B) (C) (D) v sin v cos v tan v cot

5.

The equation of a projectile is y 3 x

tan

(A) 6.

1 3

(B)

gx 2 . The angle of projection is given by : 2 (C) tan 3 2

(D)

zero

A projectile of mass m is thrown with a velocity v making an angle of 45 with the horizontal. The change in momentum from departure to arrival along vertical direction, is : mv (A) 2 mv (B) (C) mv (D) 2 mv 2

Paragraph for Q.7 - 10 A stone is projected horizontally off a cliff with velocity 10 m/s. It lands at a distance 'd ' from the foot of the cliff after 6 second. Take g = 10 m/s2

u 10 ms 1

B h

Cliff d

7.

The height of the cliff is___. (A) 60 m (B)

VMC/Motion in Two Dimension

120 m

(C)

180 m

53

(D)

240 m

HWT/Physics

Vidyamandir Classes 8.

9.

10.

The distance 'd ' is_____. (A) 60 m

(B)

45 m

(C)

30 m

The velocity of the stone at the time of impact with the ground is_____. (A) 10 m/s (B) 70 m/s (C) 60.8 m/s

(D)

15 m

(D)

70.2 m/s

(D)

3 s 2

The stone is moving with double its initial speed at time______. (A)

2s

VMC/Motion in Two Dimension

(B)

1s

(C)

3s

54

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : M2D [9]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

A projectile shot into air at some angle with the horizontal has a range of 200 m. If the time of flight is 5 s, then the horizontal component of the velocity of the projectile at the highest point of trajectory is : (A)

40 ms 1

(C)

9.8 ms 1

4.

5.

(D)

Equal to the velocity of projection of the projectile

If the angle of projection of a projectile is 30 , then how many times the horizontal range is larger than the maximum height ? 2

(B)

3

(C)

3 4

(D)

4 3

A particle is projected from the ground with an initial speed of v at an angle with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is : v v v 1 2 cos 2 1 cos 2 1 3 cos 2 (A) (B) (C) (D) v cos 2 2 2 3 The equation of motion of a projectile is y 12 x x 2 . The horizontal component of velocity is 3ms 1 . What is the range of the 4 projectile ? (A) 18 m (B) 16 m (C) 12 m (D) 21.6 m

v-t graph for a projectile, where v is vertical component of velocity, is____.

v

v

(A)

v

(B)

v

(C)

t 6.

0 ms 1

(A) 3.

(B)

(D)

t

t

Range of a projectile with time of flight 10 s and maximum height 100 m is : (g = 10 m/s2) (A) 200 m (B) 125 m (C) 100 m (D)

t

Data incorrect

Paragraph for Q.7 - 10 A ball is thrown upwards from the top of an incline with angle of projection with the vertical. If 60 , and g = 10 m/s2.

u 10 m / s

30m

7.

The time of flight is______. (A) (B) t 3s

VMC/Motion in Two Dimension

t4s

t 3s

(C)

55

(D)

t6s

HWT/Physics

Vidyamandir Classes 8.

The angle if the ball lands exactly at the foot of the incline is____. (A)

9.

(B)

tan 1 6

tan 1

(C)

3/2

(D)

tan 1 2 3

A ball moves in a circular slot with angular acceleration 2 rad / s 2 , the angle between its velocity and acceleration is_____. (A)

10.

tan 1 3

90

(B)

tan 1 (2t ) 2

t tan 1 2

(C)

(D)

45

A particle moves along a parabolic path y = ax2 such that x component of the velocity is constant, say c. The acceleration of this particle is_____. 2ac 2 ˆj ac 2 ˆj (A) (B) (C) 2ac 2 kˆ (D) ac kˆ

VMC/Motion in Two Dimension

56

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : M2D [10]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A particle is projected from a point A with velocity u 2 an angle of 45 with horizontal as shown in figure. It strikes the plane BC at right angles. The velocity of the particle at the time of collision is : (A) (C)

2.

(B)

u 2

(D)

u

u 2

60

45

A

B

An airplane, diving at an angle of 53.0 with the vertical releases a projectile at an altitude of 730 m. The projectile hits the ground 5.00 s after being released. What is the speed of the aircraft ? (A)

3.

3u 2 2u 3

C

282 ms 1

202 ms 1

(B)

182 ms 1

(C)

(D)

102 ms 1

A particle A is projected from the ground with an initial velocity of 10 ms 1 at an angle of 60 with horizontal. From what height h should an another particle B be projected horizontally with velocity 5 ms 1 so that both the particle collide in ground at point C if both

are projected simultaneously ? g 10 ms 2

B

5ms 1 10 ms 1

h 60

A (A) 4.

C

10 m

(B)

30 m

(C)

15 m

A very broad elevator is going up vertically with a constant acceleration of 2 ms

(D) 2

25 m

. At the instant when its velocity is 4 ms 1 a ball is

projected from the floor of the list with a speed of 4 ms 1 relative to the floor at an elevation of 30 . The time taken by the ball to return

the floor is : g 10 ms 2 (A) 5.

1/2 s

(B)

1/3 s

(C)

1/4 s

(A)

10.6 m

(B)

12.8 m

(C)

15.4 m

(D)

24.2 m

(C)

45

(D)

45

(D)

2g R 3

Range is maximum for angle of projection : (A)

7.

1s

A particle is projected from the ground at an angle of 60 with horizontal with speed u 20 ms 1 . The radius of curvature of the path of the particle, when its velocity makes an angle of 30 with horizontal is : g 10 ms 2

6.

(D)

30 60

(B)

45

For a fixed range of projectile, 'R', the minimum velocity of projection is______. (A)

gR

VMC/Motion in Two Dimension

(B)

2 gR

2g R

(C)

57

HWT/Physics

Vidyamandir Classes 8.

A man in a moving bus drops a bag from a height 2 m. The bag lands on the ground with a velocity 10 m/s. The velocity of the bus at the moment he dropped the bag was_____. (A)

9.

10.

10 m/s

(B)

2 10 m / s

The time it takes the bag to reach the ground is_____. 1 2 (A) (B) s s 5 5

(C)

2 15 m / s

2 s 5

(C)

(D)

5 m/s

(D)

2 5s

A boy throws a ball upwards with velocity v at an angle with the horizontal and immediately starts running. How fast must he run to catch the ball ? (A) (B) (C) (D) v/2 v cos v sin v tan

VMC/Motion in Two Dimension

58

HWT/Physics

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