The Bronx High School of Science Physics - Exam

Transcription

1 The Bronx High School of Science Physics - Exam Base your answers to questions 1 through 3 on the following information. In the diagram below, a 10.- kilogram sphere, A, is projected horizontally with a velocity of 30. meters per second due east from a height of 20. meters above level ground. At the same instant, a 20.-kilogram sphere, B, is projected horizontally with a velocity of 10. meters per second due west from a height of 80. meters above level ground. [Neglect air friction.] Version A 1. Initially, the spheres are separated by a horizontal distance of 100. meters. What is the horizontal separation of the spheres at the end of 1.5 seconds? (A) 40. m (C) 45 m (B) 15 m (D) 30 m 2. The magnitude of the horizontal acceleration of sphere A is (A) 0.0 m/s 2 (C) 9.8 m/s 2 (B) 2.0 m/s 2 (D) 15 m/s 2 3. Compared to the vertical acceleration of sphere A, the vertical acceleration of sphere B is (A) the same (C) one-half as great (B) twice as great (D) four times as great Version A Page 1

2 Base your answers to questions 4 and 5 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.] 4. At the instant the snowball is released, the horizontal component of its velocity is approximately (A) 23 m/s (B) 9.8 m/s (C) 6.9 m/s (D) 17 m/s 5. Approximately how far above the level ground does the snowball hit the smokestack? (A) 0.4 m (B) 2.4 m (C) 0.0 m (D) 4.5 m 6. 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.] 7. 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 increases, and its horizontal speed increases. (B) Its vertical speed remains the same, and its horizontal speed increases. (C) Its vertical speed increases, and its horizontal speed remains the same. (D) Its vertical speed remains the same, and its horizontal speed remains the same. Which action would most likely increase the time of flight of a ball fired by the cannon? (A) giving the ball a greater initial horizontal velocity (B) moving the cannon closer to the edge of the cliff (C) positioning the cannon higher above the ground (D) pointing the muzzle of the cannon toward the ground Version A Page 2

3 Base your answers to questions 8 through 10 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. The diagram below shows a student throwing a baseball horizontally at 25 meters per second from a cliff 45 meters above the level ground. 8. What is the horizontal velocity of the ball just before it reaches the ground? [Neglect air resistance.] (A) 34.3 m/s (C) 68.6 m/s (B) 20.0 m/s (D) 9.81 m/s 9. What is the initial vertical velocity of the ball? (A) 9.81 m/s (C) 60.0 m/s (B) 20.0 m/s (D) 0 m/s 10. What is the approximate total time required for the ball to reach the ground? [Neglect air resistance.] (A) 12.2 s (C) 3.00 s (B) 2.04 s (D) 3.50 s Approximately how far from the base of the cliff does the ball hit the ground? [Neglect air resistance.] (A) 75 m (C) 230 m (B) 140 m (D) 45 m Base your answers to questions 12 and 13 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 35º 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.] 12. The horizontal component of the ball s initial velocity is approximately (A) 7.0 m/s (C) 4.9 m/s (B) 13 m/s (D) 3.6 m/s Version A Page 3

4 13. The maximum height reached by the ball is approximately (A) 1.2 m (C) 4.9 m (B) 2.5 m (D) 8.5 m 14. A plane flying horizontally above Earth s surface at 100. meters per second drops a crate. The crate strikes the ground 30.0 seconds later. What is the magnitude of the horizontal component of the crate s velocity just before it strikes the ground? [Neglect friction.] (A) 394 m/s (C) 294 m/s (B) 0 m/s (D) 100. m/s Base your answers to questions 15 through 19 on the information below. A ball is projected vertically upward from the surface of the Earth with an initial speed of +49 meters per second. The ball reaches its maximum height in 5.0 seconds. (Disregard air resistance.) 15. Which graph best represents the relationship between displacement and time for the motion of the ball? (A) (C) 18. What is the total displacement of the ball from the time it is thrown until it returns to the point from which it was thrown? (A) 9.8 m (C) 0 m (B) 248 m (D) 49 m 19. Which graph best represents the relationship between velocity and time for the motion of the ball? (A) (B) (C) (D) 20. A rock is thrown horizontally from the top of a cliff at 12 meters per second. Approximately how long does it take the rock to fall 45 meters vertically? [Assume negligible air resistance.] (A) 1.0 s (C) 3.0 s (B) 5.0 s (D) 8.0 s 21. Above a flat horizontal plane, an arrow, A, is shot horizontally from a bow at a speed of 50 meters per second, as shown in the diagram below. A second arrow, B, is dropped from the same height and at the same instant as A is fired. (B) (D) 16. What is the maximum height reached by the ball? (A) m (C) 245 m (B) 49.0 m (D) 24.5 m 17. What is the velocity of the ball just as it returns to the point from which it was thrown? (A) +49 m/s (C) 0 m/s (B) 49 m/s (D) 9.8 m/s Neglecting air friction, compared to the amount of time A takes to strike the plane, the amount of time B takes to strike the plane is (A) less (C) the same (B) greater Version A Page 4

5 22. 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 (C) 9.8 s (B) 2.0 s (D) 4.0 s 23. A book is pushed with an initial horizontal velocity of 5.0 meters per second off the top of a desk. What is the initial vertical velocity of the book? (A) 2.5 m/s (C) 0 m/s (B) 10. m/s (D) 5.0 m/s Base your answers to questions 24 and 25 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.] 24. How many seconds does the ball take to reach the ground? (A) 2.0 s (C) 9.8 s (B) 20. s (D) 4.5 s 25. During the flight of the ball, what is the direction of its acceleration? (A) westward (C) upward (B) downward (D) eastward 26. A 2-kilogram block is dropped from the roof of a tall building at the same time a 6-kilogram ball is thrown horizontally from the same height. Which statement best describes the motion of the block and the motion of the ball? [Neglect air resistance.] (A) The 6-kg ball hits the ground first because it has more mass. (B) The 2-kg block hits the ground first because it has no horizontal velocity. (C) The 6-kg ball hits the ground first because it is round. (D) The block and the ball hit the ground at the same time because they have the same vertical acceleration. 27. A red ball and a green ball are simultaneously thrown horizontally from the same height. The red ball has an initial speed of 40. meters per second and the green ball has an initial speed of 20. 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 will be (A) the same (C) half as much (B) four times as much (D) twice as much Base your answers to questions 28 and 29 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. 28. The time it takes projectile B to reach the level surface is (A) 4.5 s (C) 3.0 s (B) 2.0 s (D) 10. s 29. Approximately how high is the cliff? (A) 44 m (C) 29 m (B) 60. m (D) 104 m Version A Page 5

6 30. The diagram below represents the path of an object after it was thrown. Base your answers to questions 34 through 36 on the diagram below which represents a ball being kicked by a foot and rising at an angle of 30.º from the horizontal. The ball has an initial velocity of 5.0 meters per second. [Neglect friction.] What happens to the object s acceleration as it travels from A to B? [Neglect friction.] (A) It decreases. (C) It remains the same. (B) It increases. 31. 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) four times as great (C) the same (B) twice as great (D) one-half as great 32. A 0.25-kilogram baseball is thrown upward with a speed of 30. meters per second. Neglecting friction, the maximum height reached by the baseball is approximately (A) 74 m (C) 15 m (B) 92 m (D) 46 m 33. Which graph best represents the relationship between the velocity of an object thrown straight upward from Earth s surface and the time that elapses while it is in the air? [Neglect friction.] 34. What is the magnitude of the horizontal component of the ball's initial velocity? (A) 2.5 m/s (C) 4.3 m/s (B) 5.0 m/s (D) 8.7 m/s 35. As the ball rises, the vertical component of its velocity (A) decreases (C) remains the same (B) increases 36. If the angle between the horizontal and the direction of the 5.0-meters-per-second velocity decreases from 30.º to 20.º, the horizontal distance the ball travels will (A) decrease (C) remain the same (B) increase Base your answers to questions 37 through 39 on the information and diagram below. (A) (C) A cannon elevated at an angle of 35º to the horizontal fires a cannonball, which travels the path shown in the diagram below. [Neglect air resistance and assume the ball lands at the same height above the ground from which it was launched.] (B) (D) 37. If the ball lands meters from the cannon 10. seconds after it was fired, what is the horizontal component of its initial velocity? (A) 35 m/s (C) 7.0 m/s (B) 70. m/s (D) 49 m/s Version A Page 6

7 38. If the ball's time of flight is 10. seconds, what is the vertical component of its initial velocity? (A) 98 m/s (C) 70. m/s (B) 49 m/s (D) 9.8 m/s 39. If the angle of elevation of the cannon is decreased from 35º to 30.º, the vertical component of the ball's initial velocity will (A) increase and its horizontal component will decrease (B) decrease and its horizontal component will decrease (C) increase and its horizontal component will increase (D) decrease and its horizontal component will increase Base your answers to questions 40 and 41 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. 42. 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) 36 m/s (C) 48 m/s (B) 40. m/s (D) 30. m/s 43. A bullet is fired from a rifle with a muzzle velocity of 100. meters per second at an angle of 30. above the horizontal. What is the magnitude of the vertical component of the muzzle velocity? (A) 0.0 m/s (C) 87. m/s (B) 50. m/s (D) 100. m/s 44. A projectile is fired with a velocity of 150. meters per second at an angle of 30º with the horizontal. What is the magnitude of the vertical component of the velocity at the time the projectile is fired? (A) 225 m/s (C) 75.0 m/s (B) 150. m/s (D) 130. m/s 45. An object is thrown into the air and follows the path shown in the diagram above. Which vector best represents the acceleration of the object at point A? [Neglect air friction.] (A) (C) (B) (D) 40. What is the total horizontal distance traveled by the golf ball during the first 2.50 seconds of its flight? (A) 64.3 m (C) 100. m (B) 76.6 m (D) 40.0 m 41. What is the vertical component of the golf ball s initial velocity? (A) 61.3 m/s (C) 40.0 m/s (B) 25.7 m/s (D) 30.6 m/s 46. A projectile is launched at an angle of 60 above the horizontal. Compared to the vertical component of the initial velocity of the projectile, the vertical component of the projectile's velocity when it has reached its maximum height is (A) less (C) the same (B) greater Version A Page 7

8 Base your answers to questions 47 and 48 on the information and diagram below. A projectile is launched at an angle of 60.º above the horizontal at an initial speed of 40. meters per second, as shown in the diagram below. The projectile reaches its highest altitude at point P and strikes a target at point T. [Neglect air resistance.] 48. Which graph best represents the horizontal speed of the projectile as a function of time? [Neglect air resistance.] (A) (B) 47. What is the magnitude of the vertical component of the projectile's initial speed? (A) 4.3 m/s (C) 9.8 m/s (B) 20 m/s (D) 35 m/s (C) (D) Version A Page 8

9 Base your answers to questions 49 through 51 on on the diagram and information below. A machine launches a tennis ball at an angle of 45 with the horizontal, as shown. The ball has an initial vertical velocity of 9.0 meters per second and an initial horizontal velocity of 9.0 meters per second. The ball reaches its maximum height 0.92 second after its launch. [Neglect air resistance and assume the ball lands at the same height above the ground from which it was launched.] 49. The speed of the tennis ball as it leaves the launcher is approximately (A) 8.3 m/s (B) 4.5 m/s (C) 18 m/s (D) 13 m/s 50. The total horizontal distance traveled by the tennis ball during the entire time it is in the air is approximately (A) 23 m (B) 4.1 m (C) 17 m (D) 8.3 m 51. The speed at which the launcher fires tennis balls is constant, but the angle between the launcher and the horizontal can be varied. As the angle is decreased from 45 to 30., the range of the tennis balls (A) decreases (B) increases (C) remains the same 52. 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 shorter horizontal range (B) shorter flight time and longer horizontal range (C) shorter flight time and shorter horizontal range (D) longer flight time and longer horizontal range 53. 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) 90 (C) 45 (B) 60 (D) A ball is thrown at an angle of 38 to the horizontal. What happens to the magnitude of the ball s vertical acceleration during the total time interval that the ball is in the air? (A) It remains the same. (B) It increases, then decreases. (C) It decreases, then increases. (D) It decreases, then remains the same. 55. 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) 24 m/s (C) 9.8 m/s (B) 0.0 m/s (D) 3.1 m/s 56. A golf ball is hit at an angle of 45 above the horizontal. What is the acceleration of the golf ball at the highest point in its trajectory? [Neglect friction.] (A) 6.9 m/s 2 horizontal (C) 9.8 m/s 2 upward (B) 0.0 m/s 2 (D) 9.8 m/s 2 downward Version A Page 9

10 57. Four cannonballs, each with mass M and initial velocity V, are fired from a cannon at different angles relative to the Earth. Neglecting air friction, which angular direction of the cannon produces the greatest projectile height? (A) 45º (C) 20º (B) 90º (D) 70º 58. The diagram below shows a baseball being hit with a bat. Angle θ represents the angle between the horizontal and the ball's initial direction of motion. 59. The diagram below shows a golf ball being struck by a club. The ball leaves the club with a speed of 40. meters per second at an angle of 60. with the horizontal. Which value of θ would result in the ball traveling the longest horizontal distance? [Neglect air resistance.] (A) 60º (C) 30º (B) 75º (D) 45º If the ball strikes the ground 7.1 seconds later, how far from the golfer does the ball land? [Assume level ground and neglect air resistance.] (A) 280 m (C) 35 m (B) 140 m (D) 71 m 60. 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) 10. s (C) 20. s (B) 100. s (D) 5.0 s 61. A basketball player jumped straight up to grab a rebound. If she was in the air for 0.80 second, how high did she jump? (A) 0.50 m (C) 3.1 m (B) 1.2 m (D) 0.78 m Version A Page 10

11 Answer Key Projectile motion AW [Nov 01, 2010] 1. A 2. A 3. A 4. A 5. B 6. C 7. C 8. B 9. D 10. D 11. A 12. C 13. A 14. D 15. D 16. A 17. B 18. C 19. A 20. C 21. C 22. B 23. C 24. D 25. B 26. D 27. A 28. C 29. A 30. C 31. C 32. D 33. A 34. C 35. A 36. A 37. B 38. B 39. D 40. B 41. B 42. C 43. B 44. C 45. A 46. A 47. D 48. A 49. D 50. C 51. A 52. B Version A

12 Answer Key Projectile motion AW [Nov 01, 2010] 53. C 54. A 55. B 56. D 57. B 58. D 59. B 60. A 61. D Version A