IB Questions on Projectile Motion

IB questions on Topic 9.1_Projectile Motion

1.

The diagram below shows the path of a projectile in the absence of air resistance. V e r t i c a l p o s i t i o n

H

o

r i z o

n

t a l

p

o

s i t i o

n

Which one of the following diagrams best represents the path of the projectile under the same initial conditions when the air resistance is taken into account? (The path in absence of air resistance is shown for comparison as a dotted line.) A

.V e r t i c a l p o s i t i o n

B

H C

o

r i z o

n

. V e r t i c a l p o s i t i o n

. V e r t i c a l p o s i t i o n

t a l D

H

o

r i z o

n

p

o

s i t i o

n

H

o

r i z o

n

t a l

p

o

s i t

H

o

r i z o

n

t a l

p

o

s i t

.V e r t i c a l p o s i t i o n

t a l

p

o

s i t i o

n

(1)

2.

Which one of the following is a true statement concerning the vertical component of the velocity and the acceleration of a projectile when it is at its maximum height? (The acceleration of free fall is g.) Vertical component of velocity

Acceleration

A.

maximum

zero

B.

maximum

g

C.

zero

zero

D.

zero

g (1)

1

3.

A stone is thrown at an angle to the horizontal. Ignoring air resistance, the horizontal component of the initial velocity of the stone determines the value of A.

range only.

B.

maximum height only.

C.

range and maximum height.

D.

range and time of flight. (1)

4.

A ball is thrown horizontally from the top of a cliff. Air resistance is negligible. Which of the following diagrams best represents the subsequent path of the ball? A

C

.

.

B

D

.

.

(1)

2

5.

A stone is projected horizontally from the top of a cliff. Neglecting air resistance, which one of the following correctly describes what happens to the horizontal component of velocity and to the vertical component of velocity? Horizontal component of velocity

Vertical component of velocity

A.

Decreases

Increases

B.

Decreases

Constant

C.

Constant

Constant

D.

Constant

Increases (1)

6.

Two identical metal spheres X and Y are released at the same time from the same height above the horizontal ground. Sphere X falls vertically from rest. Sphere Y is projected horizontally as shown below. X

Y

g

r o

u

n

d

Air resistance is negligible. Which of the following statements is correct? A.

Sphere X hits the ground before sphere Y because it travels a shorter distance.

B.

Sphere Y hits the ground before sphere X because its initial velocity is greater.

C.

The spheres hit the ground at the same time because horizontal motion does not affect vertical motion.

D.

The spheres hit the ground at the same time because they have equal weights. (1)

3

8.

The diagram below shows the trajectory of a ball thrown into the air. There is no air resistance. t r a j e c t o

r y

o

f

b

a l l

X A

B C D

Which arrow gives the direction of the resultant force on the ball at the point X? A.

A

B.

B

C.

C

D.

D (1)

4

9.

A stone is thrown from the top of a cliff with speed v at an angle θ above the horizontal, as shown.

c l i f f

Air resistance is negligible and the acceleration of free fall is g. What is the horizontal velocity of the stone a time t after the stone has been thrown? A.

v sinθ

B.

v sinθ – gt

C.

v cosθ

D.

v cosθ – gt (1)

10.

A particle is projected horizontally with speed v from a height H. It lands a horizontal distance R from the point of launch as shown in the diagram below. v

H

R A second particle is projected horizontally from the same height with speed 2v. Neglecting air resistance the horizontal distance travelled by this particle is A. B.

R. 2R.

C.

2R.

D.

4R. (1) 5

11.

This question is about projectile motion. A small steel ball is projected horizontally from the edge of a bench. Flash photographs of the ball are taken at 0.10 s intervals. The resulting images are shown against a scale as in the diagram below. d i s t a n c e / c m 0 2 0 4 0 6 0 8 0 1 0 0 0

d

2

0

4

0

6

0

i s t a n

c e 8

(a)

/

c m

0

1

0

0

1

2

0

1 4 0 Use the diagram to determine (i)

the constant horizontal speed of the ball. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2)

(ii)

the acceleration of free fall. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) 6

(b)

Mark on the diagram the position of the ball 0.50 s after projection. In the space below, you should carry out any calculations so that you can accurately position the ball. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3)

(c)

A second ball is projected from the bench at the same speed as the original ball. The ball has small mass so that air resistance cannot be neglected. Draw on the diagram the approximate shape of the path you would expect the ball to take. (3) (Total 10 marks)

12.

This question is about projectile motion. A stone of mass 0.44 kg is thrown horizontally from the top of a cliff with a speed of 22 m s as shown below. 2

3

2

2

–

m1

–1

s

mc l i f f

s e a

l e v

e l

The cliff is 32 m high. (a)

Calculate the total kinetic energy of the stone at sea level assuming air resistance is negligible. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (3)

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(b)

In practice, air resistance is not negligible. During the motion of the stone from the top of the cliff to sea level, 34% of the total energy of the stone is transferred due to air resistance. Determine the speed at which the stone reaches sea level. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (2) (Total 5 marks)

13.

This question is about trajectory motion. Antonia stands at the edge of a vertical cliff and throws a stone upwards at an angle of 60° to the horizontal. v 6

0

8= . 0

–

m1

s

°

S

e a

–1

The stone leaves Antonia’s hand with a speed v = 8.0 m s . The time between the stone leaving Antonia’s hand and hitting the sea is 3.0 s. –2

The acceleration of free fall g is 10 m s and all distance measurements are taken from the point where the stone leaves Antonia’s hand. Ignoring air resistance calculate (a)

the maximum height reached by the stone. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3)

8

(b)

the horizontal distance travelled by the stone. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (Total 5 marks)

14.

This question is about projectile motion. A stone is thrown horizontally from the top of a vertical cliff of height 33 m as shown below. 1

3

3

8

–

m1

s

m

s e a

l e v

e l

–1

The initial horizontal velocity of the stone is 18 m s and air resistance may be assumed to be negligible. (a)

State values for the horizontal and for the vertical acceleration of the stone. Horizontal acceleration: ............................................................................................ Vertical acceleration: ................................................................................................ (2)

(b)

Determine the time taken for the stone to reach sea level. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (2)

(c)

Calculate the distance of the stone from the base of the cliff when it reaches sea level. ................................................................................................................................... ................................................................................................................................... (1) (Total 5 marks)

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15.

This question is about the trajectory of a golf ball. A golfer hits a golf ball at point A on a golf course. The ball lands at point D as shown on the diagram. Points A and D are on the same horizontal level.

3

0

–

m 2

1

s 0

–

m

1

s

A

D –1

The initial horizontal component of the velocity of the ball is 20 m s and the initial vertical –1 component is 30 m s . The time of flight of the golf ball between point A and point D is 6.0 s. –2 Air resistance is negligible and the acceleration of free fall g = 10 m s . Calculate (a)

the maximum height reached by the golf ball. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (3)

(b)

the range of the golf ball. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (2) (Total 5 marks)

16.

This question is about projectile motion. –1

A stone is projected horizontally from the top of a cliff with a speed 15 m s . 1

7

0

5

–

m1

s

m

s e a 10

–2

The height of the cliff is 70 m and the acceleration of free fall is 10 m s . The stone strikes the surface of the sea at velocity V. (a)

–1

Ignoring air resistance, deduce that the stone strikes the sea at a speed of 40 m s . ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (2)

(b)

Use your answer in (a) to calculate the angle that the velocity V makes with the surface of the sea. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (2) (Total 4 marks)

17.

This question is about projectile motion. A marble is projected horizontally from the edge of a wall 1.8 m high with an initial speed V. V

1

. 8

m

g

r o

u

n

d

11

A series of flash photographs are taken of the marble. The photographs are combined into a single photograph as shown below. The images of the marble are superimposed on a grid that shows the horizontal distance x and vertical distance y travelled by the marble. The time interval between each image of the marble is 0.10 s.

0

0

. 5

0

x / m 1 . 0

1

. 5

2

. 0

0

–

y /

(a)

0

. 5

m –

1

. 0

–

1

. 5

–

2

. 0

0

On the images of the marble at x = 0.50 m and x = 1.0 m, draw arrows to represent the horizontal velocity VH and vertical velocity VV. (2)

(b)

On the photograph, draw a suitable line to determine the horizontal distance d from the base of the wall to the point where the marble hits the ground. Explain your reasoning. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3)

(c)

Use data from the photograph to calculate a value of the acceleration of free fall. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (Total 8 marks)

12

18.

This question is about projectile motion. The barrel of a rifle is held at an angle θ to the horizontal. A bullet fired from the rifle leaves –1 the barrel at time t = 0 with a speed 200 m s . The graph below shows the variation with time t of the vertical height h of the bullet. 6 0 0

h /

5

0

0

4

0

0

m 3

0

0

2

0

0

1

0

0

0 (a)

0

5

1

0

1

5

2

0

2

5

t / s Using the axes below, draw a sketch graph to show the variation of h with the horizontal distance x travelled by the bullet. (Note: this is a sketch graph; you do not have to add any values to the axes.) h

x (2) (b) State the expression for the initial vertical component of speed Vv in terms of the initial speed of the bullet and the angle θ .

................................................................................................................................... (c)

Use data from the graph to deduce that the angle θ = 30°. (The acceleration for free fall –2 g = 10 m s )

(1)

................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (3) (Total 6 marks) 13

19.

This question is about projectile motion. –1

A ball is projected from ground level with a speed of 28 m s at an angle of 30° to the horizontal as shown below.

w

3 °0 1

6

a l hl

m

There is a wall of height h at a distance of 16 m from the point of projection of the ball. Air resistance is negligible. (a)

Calculate the initial magnitudes of (i)

the horizontal velocity of the ball; ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (1)

(ii)

the vertical velocity of the ball. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (1)

(b)

The ball just passes over the wall. Determine the maximum height of the wall. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (3) (Total 5 marks)

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