Projectile Motion applications

Transcription

1 Projectile Motion applications 1. A stone is thrown horizontally at a speed of 10.0 m/s from the top of a cliff 78.4 m high. a. How long does it take the stone to reach the bottom of the cliff? b. How far from the base of the cliff does the stone strike the ground? 2. A steel projectile is shot horizontally at 20.0 m/s from the top of a 49.0-m high tower. How far from the base of the tower does the projectile hit the ground? 3. A metal ball with a constant speed of m/s rolls off the edge of a table. The table is meter high. How far from the edge of the table does the ball land? 4. A person standing on a cliff throws a stone with a horizontal speed of 15.0 m/s, and it hits the ground 47.0 m from the base of the cliff. How high is the cliff? 5. A projectile is launched horizontally from the top of a building with a speed of 12.7 m/s. What is the vertical displacement of the projectile if the projectile lands 15.0 m from the side of the building? 6. An arrow is fired horizontally from a bow, directly at the bull s-eye of a target 60.0 m away. When it is fired, the arrow is 1.00 m above the ground. If the arrow strikes the ground 20.0 m short of the target, with what speed did it leave the bow? 7. A stone is thrown horizontally at 8.0 m/s from a cliff 78.4 m high. How far from the base of the cliff will the stone strike the ground? 8. A bridge is m above a river. If a lead-weighted fishing line is thrown from the bridge with a horizontal speed of 22 m/s, what horizontal distance will it travel before striking the water? 9. A 25-lb. frozen turkey is launched horizontally out of a helicopter hovering m above the ground. a. If it travels a horizontal distance of 55 m before hitting the ground, with what speed was it heaved from the helicopter? b. With what velocity does it hit the ground? 10. Cliff divers in Acapulco dive from a cliff that is 61 m high. If the rocks below the cliff extend outward for 23 m, what is the minimum horizontal speed a diver must have to clear them?

2 11. A bullet leaves a horizontally-oriented gun with a speed of 8.0 x 10 2 m/s and hits a target 180 m away. How far does the bullet fall before it hits the target? 12. A student threw a ball horizontally out of a window 8.0 m above the ground. It was caught 1.5 m above the ground by another student who was 10.0 m away. a. What was the initial speed of the ball? b. What was the speed of the ball when it was caught? 13. During a movie scene, a motorcycle is to drive off the roof of a 44-m tall building and land on the roof of a second building that is 15 m away from the first one. If the motorcycle leaves the first roof traveling horizontally at 65 mi/hr and just barely lands on the second rooftop, how tall is the second building? 14. A projectile is fired upward from level ground with a velocity of 196 m/s, 60 above the horizontal. It lands on the ground. Calculate: a. the vertical and horizontal components of the original velocity b. the time the projectile is in the air c. the horizontal distance the projectile travels 15. A projectile is fired upward from the ground. The vertical component of its velocity is 49 m/s, and the horizontal component of its velocity is 61 m/s. a. If it lands back on the ground, how long does the projectile remain in the air? (Assume level ground.) b. What horizontal distance does it travel? c. What was the original velocity of the projectile? d. What is the maximum height the projectile reaches during its flight? 16. A mortar shell is fired at an angle of 53 above the horizontal across level ground. The launch speed of the shell is 2.00 x 10 2 m/s. Calculate a. the time the shell remains in the air. b. the horizontal distance the shell travels. c. the velocity of the shell when it strikes the ground. 17. A golf ball lying on a level fairway is hit at an angle of 45 to the horizontal. If the speed with which the ball leaves the club is 52 m/s, how far will it travel horizontally before striking the ground?

3 18. A potato is fired from a potato gun held at an angle of 37 to the horizontal. If the potato travels a horizontal distance of 245 m, what was its launch speed (assuming its landing height equals its launch height)? 19. A baseball is hit at 30.0 m/s at an angle of 53 above the horizontal. An outfielder runs at 4.0 m/s toward the infield and catches the ball. What was the original distance between the batter and the fielder? (Assume vertical displacement of ball is zero.) 20. A camper dives from the edge of the camp swimming pool at water level with a speed of 8.0 m/s at an angle of 30 above the horizontal. a. How long is the diver in the air? b. What is the diver s maximum height above the water during the dive? c. What is the diver s speed at her highest point? d. How far out in the pool does the diver land? e. With what speed does she hit the water? 21. In 1926 Babe Ruth hit a home run that was estimated to have landed 180. meters from home plate and to have reached a height of 21.3 meters. What was the initial velocity of the ball? 22. A broad jumper begins his jump at an angle of 22 from the horizontal. At the middle of the jump he reaches a height of 70.0 cm. a. What is his horizontal velocity? b. How far does he jump? 23. A cannon on the ground is fired with a velocity of 55.0 m/s at an angle of 39 above the horizontal. Calculate a) the range of the cannonball, b) the velocity of the cannonball when it hits the ground, and c) the maximum height it reaches during its flight. (Assume level ground.) 24. A daring motocross rider decides to use a 25 ramp to jump 40 garbage cans. If the cyclist was in the air for 1.8 second, calculate a) the maximum height reached by the bike, b) the velocity of the bike when it left the ramp, and c) the average diameter of the garbage cans used. (Assume vertical displacement is zero.) 25. Hockey legend Mario Lemieux cranks up a slap shot with an initial velocity of 45 m/s. If he is standing 40. meters from the goal, at what launch angle must the puck have left the ground in order for it to have just hit the ice at the goal line? How high off the ground was the puck at its highest point?

4 26. A stuntman uses a trampoline to jump over a wall 25-foot wall. If the trampoline is situated 8.0 feet from the base of the wall, calculate the speed with which he must leave the trampoline in order to just clear the wall. 27. A baseball was hit at 43.0 m/s at an angle of 25 above the horizontal. a. How long did it remain in the air (assume equal starting and ending heights)? b. How far horizontally did it travel? c. If the ball was originally 1.50 m above the playing field when it left the bat, flew out of the ball park and landed in a spot 4.50 m below the level of the playing field, what horizontal distance did it travel? 28. A projectile traveling at a speed of 100. m/s leaves the earth at an angle of 37 above the horizontal. What horizontal distance has it traveled when it is 150. m high? 29. Firefighters are fighting a fire at a building. The water exits the hose at 20. m/s, and the firefighters hold the hose 1.0 m off the ground. Assuming the nozzle makes an angle of 45 to the ground, how close must they get to the building in order to hit a window on the 3 rd story (6.0 meters off the ground)? 30. Referring to item 29: calculate a) the lowest speed the water has during its flight and b) the maximum height of the water above the ground. 31. A plane diving at an angle of 53 to the horizontal releases a projectile at an altitude of 735 m. The projectile hits the ground 5.00 s after being released. Calculate a) the speed of the plane, b) the horizontal distance traveled by the projectile during its flight, and c) the speed of the projectile as it hit the ground. 32. A marble is shot from a slingshot from the top of a building 25.0 meters high. If the marble leaves the slingshot traveling 50.0 m/s at an angle of 30 below the horizontal, calculate a) the horizontal distance it lands from the base of the building, and b) its velocity when it contacts the ground. 33. An acorn rolls off a house roof and falls to the ground. If the edge of the roof was inclined at a 25 angle, the acorn was traveling 2.45 m/s when it left the roof, and it landed 1.50 meters away the house (assume no eaves to the house roof), calculate the height of the roof edge above the ground.

5 34. A B-1 bomber moving at 175 m/s at an angle of 15 below the horizontal drops a bomb when it is 450. meters above the ground. Calculate a) the horizontal distance the bomb travels through the air, and b) the speed of the bomb when it hits the ground. 35. A cannonball is launched off a 35.0-meter high cliff, leaving the cannon barrel at 120. m/s, 40 above the horizontal, onto the level ground below. Calculate a) the horizontal distance traveled by the cannonball during its flight, b) the velocity of the cannonball as it contacts the ground, and c) the maximum height (above the base of the cliff) reached by the cannonball. 36. A stream of water is shot out of a hose situated at ground level. The water leaves the hose with a speed of 20.0 m/s, and the hose makes an angle of 55 to the horizontal. a) Calculate the maximum height reached by the water and the speed of the water at this point. b) Calculate the horizontal distance traveled by the water when it is 4.00 meters above the ground. c) If a building is 15.0 meters away from the hose, calculate how high up the side of the building the water strikes it. 37. A projectile launched at 20 below the horizontal takes 4.00 seconds to hit the ground, and travels a horizontal distance of 7.50 meters through the air to the landing site. Calculate a) the speed with which it was launched, and b) the distance through which it fell. ANSWERS: 1. a s b m m m m m, down m/s m m 9. a. 11 m/s b. 50. m/s, 77 below horiz m/s m 12. a. 8.7 m/s b. 14 m/s m 14. a. v x = 98.0 m/s v o (y) = 170. m/s b s c m 15. a. 1.0 x 10 1 s b. 610 m c. 78 m/s, 39 above horizontal d. 120 m 16. a. 33 s b. 4.0 x 10 3 m c m/s, 53 below horiz m m/s m 20. a s b m c. 6.9 m/s d. 5.7 m e. 8.0 m/s m/s, 25 above horiz. 22. a m/s, forward b m 23. a. 302 m b m/s, 39 below horiz. c m 24. a. 4.0 m b. 21 m/s c m 25. θ = 5.6, h = 0.98 m m/s ( 38. ft/s) 27. a s b m c. 156 m m and 703 m m 30. a. 14 m/s (occurs when water is at maximum height) b. 11 m 31. a. 153 m/s b m c. 195 m/s 32. a m b m/s, 39 below horiz m 34. a m b. 199 m/s 35. a m b. 123 m/s, 42 below horiz. c. 304 m 36. a m, 11.5 m/s b m and 35.3 m c m 37. a m/s b m