Unit 2 Review: Projectile Motion

Transcription

1 Name: Unit 2 Review: Projectile Motion Date: 1. A projectile is fired from a gun near the surface of Earth. The initial velocity of the projectile has a vertical component of 98 meters per second and a horizontal component of 49 meters per second. How long will it take the projectile to reach the highest point in its path? A) 5.0 s B) 10. s A) C) 20. s D) 100. s 2. Which graph best represents the motion of a freely falling body near the Earth's surface? C) 6. A baseball dropped from the roof of a tall building takes 3.1 seconds to hit the ground. How tall is the building? [Neglect friction.] A) 15 m B) 30. m C) 47 m D) 94 m Base your answers to questions 7 and 8 on the information and diagram below. A child kicks a ball with an initial velocity of 8.5 meters per second at an angle of 35 with the horizontal, as shown. The ball has an initial vertical velocity of 4.9 meters per second and a total time of flight of 1.0 second. [Neglect air resistance.] B) D) 3. An object starts from rest and falls freely. What is the velocity of the object at the end of 3.00 seconds? A) 9.81 m/s B) 19.6 m/s C) 29.4 m/s D) 88.2 m/s 4. A vector makes an angle,, with the horizontal. The horizontal and vertical components of the vector will be equal in magnitude if angle is A) 30 B) 45 C) 60 D) A rock is dropped from a bridge. What happens to the magnitude of the acceleration and the speed of the rock as it falls? [Neglect friction.] A) Both acceleration and speed increase. B) Both acceleration and speed remain the same. C) Acceleration increases and speed decreases. D) Acceleration remains the same and speed increases. 7. The horizontal component of the ball's initial velocity is approximately A) 3.6 m/s B) 7.0 m/s A) 1.2 m B) 2.5 m C) 4.9 m/s D) 13 m/s 8. The maximum height reached by the ball is approximately A) kinetic energy B) momentum C) 4.9 m D) 8.5 m 9. A 1-kilogram object is thrown horizontally and a 2-kilogram object is dropped vertically at the same instant and from the same point above the ground. If friction is neglected, at any given instant both objects will have the same C) total velocity D) height

2 10. A ball thrown vertically upward reaches a maximum height of 30. meters above the surface of Earth. At its maximum height, the speed of the ball is A) 0.0 m/s B) 9.8 m/s C) 3.1 m/s D) 24 m/s Base your answers to questions 13 through 15 on the information and diagram below. A ball is thrown horizontally with an initial velocity of 20.0 meters per second from the top of a tower 60.0 meters high. 11. Base your answer to the following question on the diagram below which shows a ball projected horizontally with an initial velocity of 20. meters per second east, off a cliff 100. meters high. [Neglect air resistance.] During the flight of the ball, what is the direction of its acceleration? A) downward B) upward C) westward D) eastward 12. A baseball player throws a ball horizontally. Which statement best describes the ball's motion after it is thrown? [Neglect the effect of friction.] A) Its vertical speed remains the same, and its horizontal speed increases. B) Its vertical speed remains the same, and its horizontal speed remains the same. C) Its vertical speed increases, and its horizontal speed increases. D) Its vertical speed increases, and its horizontal speed remains the same. 13. What is the horizontal velocity of the ball just before it reaches the ground? [Neglect air resistance.] A) 9.81 m/s B) 20.0 m/s A) 12.2 s B) 2.04 s C) 34.3 m/s D) 68.6 m/s 14. What is the approximate total time required for the ball to reach the ground? [Neglect air resistance.] A) 0 m/s B) 9.81 m/s C) 3.00 s D) 3.50 s 15. What is the initial vertical velocity of the ball? C) 20.0 m/s D) 60.0 m/s

3 16. A rock falls freely from rest near the surface of a planet where the acceleration due to gravity is 4.0 meters per second 2. What is the speed of this rock after it falls 32 meters? A) 8.0 m/s B) 16 m/s C) 25 m/s D) 32 m/s 17. A 0.2-kilogram red ball is thrown horizontally at a speed of 4 meters per second from a height of 3 meters. A 0.4-kilogram green ball is thrown horizontally from the same height at a speed of 8 meters per second. Compared to the time it takes the red ball to reach the ground, the time it takes the green ball to reach the ground is A) one-half as great B) twice as great C) the same D) four times as great 18. A volleyball hit into the air has an initial speed of 10. meters per second. Which vector best represents the angle above the horizontal that the ball should be hit to remain in the air for the greatest amount of time? A) C) B) D) 19. A ball dropped from rest falls freely until it hits the ground with a speed of 20 meters per second. The time during which the ball is in free fall is approximately A) 1 s B) 2 s C) 0.5 s D) 10 s

4 20. An archer uses a bow to fire two similar arrows with the same string force. One arrow is fired at an angle of 60. with the horizontal, and the other is fired at an angle of 45 with the horizontal. Compared to the arrow fired at 60., the arrow fired at 45 has a A) longer flight time and longer horizontal range B) longer flight time and shorter horizontal range C) shorter flight time and longer horizontal range D) shorter flight time and shorter horizontal range 21. The diagram below shows the muzzle of a cannon located 50. meters above the ground. When the cannon is fired, a ball leaves the muzzle with an initial horizontal speed of 250. meters per second. [Neglect air resistance.] Which action would most likely increase the time of flight of a ball fired by the cannon? A) pointing the muzzle of the cannon toward the ground B) moving the cannon closer to the edge of the cliff C) positioning the cannon higher above the ground D) giving the ball a greater initial horizontal velocity

5 22. Base your answer to the following question on the information and diagram below. A student standing on a knoll throws a snowball horizontally 4.5 meters above the level ground toward a smokestack 15 meters away. The snowball hits the smokestack 0.65 second after being released. [Neglect air resistance.] At the instant the snowball is released, the horizontal component of its velocity is approximately A) 6.9 m/s B) 9.8 m/s C) 17 m/s D) 23 m/s 23. A ball is thrown vertically upward with an initial velocity of 29.4 meters per second. What is the maximum height reached by the ball? [Neglect friction.] A) 14.7 m B) 29.4 m C) 44.1 m D) 88.1 m 24. Base your answer to the following question on the information and diagram below A golf ball leaves a golf club with an initial velocity of 40.0 meters per second at an angle of 40º with the horizontal. What is the total horizontal distance traveled by the golf ball during the first 2.50 seconds of its flight? A) 100. m B) 76.6 m C) 64.3 m D) 40.0 m

6 25. A soccer ball kicked on a level field has an initial vertical velocity component of 15.0 meters per second. Assuming the ball lands at the same height from which it was kicked, what is the total time the ball is in the air? [Neglect friction.] A) s B) 1.53 s A) 49 m B) 98 m C) 3.06 s D) After a model rocket reached its maximum height, it then took 5.0 seconds to return to the launch site. What is the approximate maximum height reached by the rocket? [Neglect air resistance.] C) 120 m D) 250 m Base your answers to questions 27 and 28 on the information below. Projectile A is launched horizontally at a speed of 20. meters per second from the top of a cliff and strikes a level surface below, 3.0 seconds later. Projectile B is launched horizontally from the same location at a speed of 30. meters per second. 27. The time it takes projectile B to reach the level surface is A) 4.5 s B) 2.0 s C) 3.0 s D) 10. s 30. A projectile is fired with an initial velocity of 120 meters per second at an angle,, above the horizontal. If the projectile's initial horizontal speed is 55 meters per second, then angle measures approximately A) 13 B) 27 C) 63 D) A ball is thrown horizontally at a speed of 20. meters per second from the top of a cliff. How long does the ball take to fall 19.6 meters to the ground? A) 1.0 s B) 2.0 s C) 9.8 s D) 4.0 s 32. A golf ball is propelled with and initial velocity of 60. meter per second at 37º above the horizontal. The horizontal component of the golf ball's initial velocity is A) 30. m/s B) 36 m/s C) 40. m/s D) 48 m/s 33. A ball is fired vertically upward at 5.0 meters per second from a cart moving horizontally to the right at 2.0 meters per second. Which vector best represents the resultant velocity of the ball when fired? A) B) C) D) 28. Approximately how high is the cliff? A) 29 m B) 44 m A) parabolic B) linear C) 60. m D) 104 m 29. The path of a projectile fired at a 30 angle to the horizontal is best described as C) circular D) hyperbolic 34. Two stones, A and B, are thrown horizontally from the top of a cliff. Stone A has an initial speed of 15 meters per second and stone B has an initial speed of 30. meters per second. Compared to the time it takes stone A to reach the ground, the time it takes stone B to reach the ground is A) the same B) twice as great C) half as great D) four times as great

7 35. Which diagram best represents the position of a ball, at equal time intervals, as it falls freely from rest near Earth's surface? A) C) B) D) 36. A projectile has an initial horizontal velocity of 15 meters per second and an initial vertical velocity of 25 meters per second. Determine the projectile s horizontal displacement if the total time of flight is 5.0 seconds. [Neglect friction.]

8 Base your answers to questions 37 through 39 on the information below. The path of a stunt car driven horizontally off a cliff is represented in the diagram below. After leaving the cliff, the car falls freely to point A in 0.50 second and to point B in 1.00 second. 37. Determine the magnitude of the horizontal component of the velocity of the car at point B. [Neglect friction.] 38. Calculate the magnitude of the vertical displacement, dy, of the car from point A to point B. [Neglect friction.] [Show all work, including the equation and substitution with units.] 39. Determine the magnitude of the vertical velocity of the car at point A.

9 Base your answers to questions 40 and 41 on the information and diagram below. An object was projected horizontally from a tall cliff. The diagram below represents the path of the object, neglecting friction. Base your answers to questions 42 through 44 on the information and diagram below. A projectile is launched horizontally at a speed of meters per second from a platform located a vertical distance above the ground. The projectile strikes the ground after time at horizontal distance from the base of the platform. [Neglect friction.] 40. How does the magnitude of the vertical component of the object s velocity at point A compare with the magnitude of the vertical component of the object s velocity at point B? 41. How does the magnitude of the horizontal component of the object s velocity at point A compare with the magnitude of the horizontal component of the object s velocity at point B? 42. Express the projectile's total time of flight,, in terms of the vertical distance,, and the acceleration due to gravity,. [Write an appropriate equation and solve it for.] 43. Calculate the horizontal distance,, if the projectile's total time of flight is seconds. [Show all work, including the equation and substitution with units.] 44. On the diagram provided, sketch the theoretical path of the projectile.

10 Base your answers to questions 45 through 47 on the information and graph below. A machine fired several projectiles at the same angle,, above the horizontal. Each projectile was fired with a different initial velocity, vi. The graph below represents the relationship between the magnitude of the initial vertical velocity, viy, and the magnitude of the corresponding initial velocity, vi, of these projectiles 45. Determine the magnitude of the initial vertical velocity of the projectile, viy, when the magnitude of its initial velocity, vi, was 40. meters per second. 46. Determine the angle,, above the horizontal at which the projectiles were fired. 47. Calculate the magnitude of the initial horizontal velocity of the projectile, vix, when the magnitude of its initial velocity, vi, was 40. meters per second. [Show all work, including the equation and substitution with units.]

11 Base your answers to questions 48 through 50 on the information below. A projectile is fired from the ground with an initial velocity of 250. meters per second at an angle of 60. above the horizontal. 48. On the diagram above, use a protractor and ruler to draw a vector to represent the initial velocity of the projectile. Begin the vector at point P, and use a scale of 1.0 centimeter = 50. meters per second. 49. Explain why the projectile has no acceleration in the horizontal direction. [Neglect air friction.] 50. Determine the horizontal component of the initial velocity.