Practice Projectiles 2

Projectile Practice Packet Free Fall Problems Getting Started

1. A lemur runs off a cliff. The cliff is 3.7 m tall. The lemur is on earth. How long will it take the lemur to hit the ground below? (Answer: 0.87 s) 2. If you were to drop a penny off the top of the Burj Kalifa (818m tall) and there was no air resistance, how fast would the penny be going when it hit the ground? (126 m/s) 3. A tourist drops a rock from rest from a guard rail overlooking a valley. a. What is the velocity of the rock at 4.0 s? (Answer: -39.2 m/s) b. What is the displacement of the rock at 4.0 s? (Answer: -78.4 m)

Prepared 4. An astronaut on the moon, where the acceleration due to gravity is -1.6 m/s/s. She drops a hammer from her hand, which is about 1.5 m off the ground. How long will it take to hit the ground? (Answer: 1.37 m/s) 5. Smashing Samantha is launched out of a rocket going straight up into the air at a velocity of 24 m/s. a. How high will she go? (29 m up) b. How long will it take her to fall back to earth? (2.4 s) c. If she were to land back in the cannon- how fast would she be going when she returns to the barrel? (24 m/s down) 6. An apple is dropped to the ground on Mars, where the acceleration due to gravity is 3.8 m/s/s. Sketch the velocity vs. time graph for the apple falling and label its slope. 7. A monkey angrily tosses poop down at an annoying tourist with a velocity of 2.6 m/s. The poop is going 10.7 m/s when it hits the tourist. a. How far did the poop fall? (-5.5 m) b. How long does the tourist have to react before the poop hits them? (0.83 s)

Jedi

8. A college student wants to toss a textbook to his roommate who is leaning out of a window directly above him. He throws the book upwards with an initial velocity of 8.0 m/s. The roommate catches it while it is travelling at 3.0 m/s [up]. a) How long was the book in the air? (0.51 s) b) How far vertically did the book travel? (2.8 m) 9. The average person can jump about 35 cm on earth. How high can this person jump on the moon, where the acceleration due to gravity is 1.62 m/s/s? (2.1 m)

Horizontal Projectiles 10. Consider these diagrams in answering the following questions.

11. Which diagram (if any) might represent ... a. ... the initial horizontal velocity? b. ... the initial vertical velocity? c. ... the horizontal acceleration? d. ... the vertical acceleration? e. ... the net force?

12. You run off a cliff going 6.8 m/s. The cliff is 22 m tall. a. How long will it take you to hit the water? (2.1 s) b. How far from the base of the cliff will you land? (14 m) 13. In an effort to create a cannonball-style splash, eight-year old Matthew runs off the edge of the board of the high dive at 4.6 m/s and falls 2.3 m to the water below. a. Determine the time for Matthew to fall the 2.3 m to the water. (Answer: 0.69 s) b. What horizontal distance from the edge of the board will Matthew plunge into the water? (Answer: 3.2 m) 14. A ball rolls with a speed of 2.0 m/s across a level table that is 1.0 m above the floor. Upon reaching the edge of the table, it follows a parabolic path to the floor. How far along the floor is the landing spot from the table? [Answer: 0.90 m] 15. A ball rolls with a speed of 2.0 m/s across a level table that is 1.0 m above the floor. Upon reaching the edge of the table, it follows a parabolic path to the floor. How far along the floor is the landing spot from the table? [Answer: 0.90 m] 16. Ima Peode wishes to throw a 2.8-kg pumpkin horizontally off the top of the school roof in order to hit Mr. H's car. The car is parked a distance of 13.4 m away from the base of the building below the point where Ima is standing. The building's roof is 10.4 m high. Assuming no air resistance, with what horizontal speed must Ima toss the pumpkin in order to hit Mr. H's car. (Answer: 9.20 m/s) 17. A skier leaves the horizontal end of a ramp with a velocity of 25.0 m/s and lands 70.0 m from the base of the ramp. How high is the end of the ramp from the ground? [Answer: Brittany Story38.5 m] 18. A ball is launched horizontally from the top of a cliff with an initial velocity of 20 m/s. The trajectory of the ball is shown below. Express your understanding by filling in the blanks. You may need a separate sheet of paper for your work.

Jedi 19. An astronaut stands on the edge of a lunar crater and throws a half-eaten Twinkie™ horizontally with a velocity of 5.00 m/s. The floor of the crater is 100.0 m below the astronaut. What horizontal distance will the Twinkie™ travel before hitting the floor of the crater? (The acceleration of gravity on the moon is 1/6th that of the Earth). [Answer: 55.3 m] 20.

Finding the final velocity of a horizontal projectile 1. A pool ball leaves a 0.20-meter high table with an initial horizontal velocity of 2.4 m/s. What is the final velocity of the pool ball? (Answer: 3.089 m/s at 29.24°)

2. I throw a ball off the edge of a 15.0m tall cliff. I threw it horizontally at 8.0m/s. What is the final velocity of the ball? (Answer: 17 m/s at 25°)

Introduction to Trig Pythagorean Practice

Intro to Trig Practice Solve for the unknowns

1.

4.

2.

3.

5.

6.

Answers: 1. a= 25 2. C=34 3. Θ=12, 4. Θ= 44, 5. θ= 53 , 6. b= 13, c=22

Initial Velocity in the x and y Break the velocity down into its x and y components 1. A water balloon is launched with a speed of 40 m/s at an angle of 60 degrees to the horizontal. (Answer: vx=20.0 m/s) 2. A projectile has an initial velocity in the x direction of 2.7 m/s and 3.6 in the y direction. a. What is the speed of the object? b. What is the velocity of the object? 3. A motorcycle stunt person traveling 70 mi/hr jumps off a ramp at an angle of 35 degrees to the horizontal. (Answer: vx = 57.3 mi/hr, vy =40.1 mi/hr) 4. A small koala jumps at a person’s face. It leaps at 15 m/s at an angle of 45 degrees.

Solving Projectile at an Angle Problems 1. A baseball player leads off the game and hits a long home run. The ball leaves the bat at an angle of 30.0o from the horizontal with a velocity of 40.0 m/s. How far will it travel in the air? [Answer: 141 m] o

2. A football is kicked at 37.0 to the horizontal at 20.0 m/s from the player’s hand at 1.00 m from the ground. How far did the football travel before hitting the ground? [Answer: 40.5 m] o 3. An object is punted at 25.0 m/s [40.0 N of E] on G’s home planet. What is the range of the 2

object on level ground? (Use g = 18.0 m/s ) [Answer: 34.2 m] 4. A lovesick lad wants to throw a bag of candy and love notes into the open window of his girlfriend’s bedroom 10.0 m above. Assuming it just reaches the window, he throws the love gifts at 60.0o to the ground: a. At what velocity should he throw the bag? [Answer: 16.2 m/s at 60.0° to the ground] b. How far from the house is he standing when he throws the bag? [Answer: 11.5 m] 5. A punter in a football game kicks a ball from the goal line at 60.0o from the horizontal at 25.0 m/s. a. What is the hang time of the punt? [Answer: 4.41 s] b. How far down field does the ball land? [Answer: 55.2 m] Jedi 6. A cannon fires a cannonball 500.0 m downrange when set at a 45.0° angle. At what velocity does the cannonball leave the cannon? [Answer: 70.0 m/s at 45.0°] 7. A golfer is teeing off on a 170.0 m long par 3 hole. The ball leaves with a velocity of 40.0 m/s at 50.0o to the horizontal. Assuming that she hits the ball on a direct path to the hole, how far from the hole will the ball land (no bounces or rolls)? [Answer: 9.38 m]