(a) On the diagram above, draw an arrow showing the direction of velocity of the projectile at point A.

Transcription

1 QUESTION 1 The path of a projectile in a uniform gravitational field is shown in the diagram below. When the projectile reaches its maximum height, at point A, its speed v is 8.0 m s -1. Assume g = 10 m s -2. The projectile passes point B 0.60 seconds after it passes point A. (a) On the diagram above, draw an arrow showing the direction of velocity of the projectile at point A. (b) Calculate the magnitudes of the vertical and horizontal components of the velocity of the projectile at point B (1 mark) (c) Calculate the magnitude of the velocity of the projectile at point B. Explain your answer with the aid of a vector diagram. (4 marks)

2 QUESTION 2 (a) The parabolic path of a small particle projected in the Earth's constant gravitational field is shown in the diagram below. Draw labelled arrows from A and B to indicate the direction of the velocity v and the acceleration, a, at each of these points. (b) A projectile is released from ground height at point A with a speed of v 0 = 12.0 m s -1, at an angle of 60.0 to the horizontal. The projectile reaches maximum height at point B and hits the ground at point C, as shown in the diagram below. Ignore air resistance. Use g = 9.80 m s -2. (i) Calculate the horizontal and vertical components of the velocity of the projectile at the instant of release.

3 (ii) Calculate the horizontal and vertical components of the velocity of the projectile at point B. (iii) Calculate the total time of flight of the projectile. (5 marks) (iv) Calculate the total horizontal distance travelled by the projectile. (4 marks)

4 (c) The diagram below shows the path of a shot released at point A by an athlete competing in a shot-put event. The shot is released with a speed of v 0 = 12.0 m s -1, at an angle of 60.0 to the horizontal (i) Explain why the shot will travel further horizontally than did the projectile in part (b). (ii) Discuss the effect on the range of the shot if the athlete releases the shot from the same height and with the same initial speed but at a larger angle to the horizontal.

5 QUESTION 3 The multi-image diagram below represents a projectile that has been thrown horizontally from the top of a cliff. The value of the acceleration due to gravity is g = 9.80 m s -2. The time interval between images is s. (a) What does the diagram indicate about the horizontal component of the velocity of the projectile? Give a reason for your answer. (b) Calculate the horizontal component of the velocity of the projectile as it travels from A to B. (c) Calculate the magnitude of the vertical component of the velocity of the projectile s after it has been thrown.

6 (d) Draw a vector diagram and use it to calculate the magnitude and direction of the velocity v of the projectile s after it has been thrown. (5 marks) (e) On the multi-image diagram opposite, sketch a possible path for the projectile if air resistance has a significant effect. (1 mark) (f) (i) Assume that the cliff is 20.0 m above the ground. Calculate the time the projectile would take to strike the ground if thrown horizontally from the top of the cliff. Ignore air resistance. (ii) State the time the projectile would take to strike the ground if thrown horizontally from the top of the cliff at twice the horizontal speed calculated in part (b). Explain your answer.

7 QUESTION 4 (a) A projectile is launched from the ground at a speed v = 30.0 m s -1 and an angle Ө = 40 above the horizontal, as shown in the diagram below. (The acceleration due to gravity g = 9.80 ms -2 ) Calculate the magnitudes of the horizontal and vertical components of the initial velocity. (4 marks) (b) The projectile is now launched with the same initial velocity from a position above the ground, as shown in the diagram below. Describe and explain the effect that launching from above the ground has on the range of this projectile in comparison with launching from the ground.

8 QUESTION 5 You are in an open-top car, travelling east along a horizontal straight road at a constant velocity of 25 ms -1. You throw a ball vertically upwards at a speed of 11 ms -1. (Ignore air resistance. Gravitational acceleration g is 9.8 ms -2 directed downwards.) (a) State the magnitude of the horizontal component of the velocity of the ball at the instant the ball leaves your hand. (1 mark) (b) Calculate the time the ball takes to return to the same height from which it was thrown. (c) Calculate the horizontal distance the ball moved during the time you calculated in part (b).

9 (d) Calculate the speed of the ball 2.0 s after it leaves your hand. (5 marks) (e) Describe and explain where the ball will land in relation to the car. (f) Describe and explain where a ball would land in relation to the car if the ball encountered significant air resistance. Assume the effect of air resistance on the car is negligible.

10 QUESTION 6 The multi-image diagram below represents the motion of a projectile launched from the ground. The time interval between images is 1.0 s. Assume negligible air resistance for the motion shown. Using the information shown in the diagram above: (a) Calculate the horizontal speed of the projectile. (b) State the maximum height reached by the projectile. (1 mark) (c) Calculate the magnitude of the vertical acceleration of the projectile.

11 QUESTION 7 A stone is thrown from a position near the surface of the Earth with an initial horizontal velocity of 25 ms -1, as shown in the diagram below. The vertical component of the velocity of the stone at point X is 36 ms -1. Assume air resistance is negligible. (a) Draw and label a vector diagram to show the addition of the horizontal and vertical components of the velocity of the stone at the instant it reaches point X. (The diagram does not need to be drawn to scale.) (b) Calculate the magnitude and direction of the velocity of the stone at point X. (5 marks)

12 (c) Describe and explain the effect that increasing the launch height of a shot-put has on the maximum range. Assume air resistance is negligible.

13 QUESTION 8 A tennis player hits a ball horizontally towards a net of height 0.90 m at an initial speed of 25 ms -1. The ball is hit at a height of 2.5 m above the ground and at a horizontal distance of 15 m from the net, as shown in the diagram below. Ignore air resistance and any effects of spin. (a) Show that the time the ball takes to reach the net is 0.60 s. (b) Hence calculate the change in the height of the ball during this time. (c) Determine the height at which the ball hits the net.

14 (d) The tennis player's aim is to hit the ball so that it passes over the net. State and explain one change that needs to be made to the way the ball is hit if the tennis player is to achieve this aim.

15 QUESTION 9 A projectile is launched from the ground with an initial velocity of 140 ms -1 at an angle Ө above the horizontal, as shown in the diagram below. Assume air resistance is negligible and the ground is level. (a) On the diagram above, show clearly how the horizontal component of velocity v H is added to the vertical component of velocity v v to give the initial velocity vector. (b) The time of flight of the projectile is measured as 18.7 s and its range as 1.98 x 10 3 m. Show that the launch angle Ө that results in this range is approximately 41. (4 marks) (c) (i) State the other launch angle that would result in the same range for this projectile. (ii) State and explain the effect of this different launch angle on the time of flight of the projectile. (1 mark)

16 QUESTION 10 A softball is hit at a height of 1.0 m above the ground with an initial velocity of 34 ms -1 at 50.0 above the horizontal, as shown in the diagram below. The ball is caught by an outfielder as it returns to a height of 1.0 m above the ground. Ignore the effects of air resistance. (a) Calculate the time the ball takes to reach the outfielder. (4 marks) (b) A tennis ball is now hit at the same height and with the same initial velocity as for the softball in part (a). The two balls are shown in the photograph below:

17 State one difference between the balls and describe how it affects the force of air resistance. (c) Two students perform a projectile motion experiment to find the launch angle that will result in the maximum range when the launch height of a projectile is above the ground. They launch a small metal ball from a projectile launcher set at a number of different launch angles. They measure the range using a sand-filled box placed at a position on the ground where they predict the ball will land. The students' experimental apparatus and their results are shown in the photograph and graph below: Discuss the variables in this experiment, clearly identifying the independent and dependent variables and at least one variable, other than launch height, that must be held constant. Using the graph, state the launch angle that results in the maximum range in this experiment, and explain why changing this angle decreases the range of the metal ball.

18 (16 marks)

19 QUESTION 11 A ball is thrown horizontally with speed v from a height of 1.9 m above the ground, as shown in the diagram below. The ball hits the ground a horizontal distance of 24 m from the initial launch position. Ignore the effects of air resistance. (a) Show that the time the ball takes to reach the ground is 0.62 s. (b) Calculate the initial speed v of the ball. (c) State the effect that air resistance would have on the range of the ball. (1 mark)

20 QUESTION 12 A baseball is thrown horizontally at a speed of 34 ms -1. The baseball travels for 0.62 s before landing on the ground. Ignore air resistance in this question. (a) State the horizontal component of velocity of the baseball when it lands, and give a reason for your answer. (b) Show that the vertical component of velocity of the baseball when it lands is 6.1 ms -1.

21 (c) Determine, with the aid of a labelled vector diagram, the direction of the velocity of the baseball when it lands on the ground. (State the angle in degrees below the horizontal.) (4 marks)

22 QUESTION 13 A projectile is launched from ground height with an initial velocity of 16.0 ms -1 at an angle of 40.0 above the horizontal, as shown in the diagram below. Ignore the effects of air resistance. (a) Show that the magnitude of the horizontal component of the initial velocity is 12.3 ms -1 and the magnitude of the vertical component of the initial velocity is 10.3 ms -1. (4 marks) (b) The time of flight of the projectile is 2.10 s. Calculate the range of the projectile. (c) (i) Calculate the vertical component of the velocity at time = 2.00 s.

23 (ii) Using a labelled vector diagram, calculate the resultant speed of the projectile at t = 2.00 s. (4 marks)

24 QUESTION 14 A javelin is thrown from a shoulder height of 1.50 m. The initial velocity of the javelin is 25.0ms -1, at an angle of 40.0 above the horizontal. Ignore air resistance in all parts of this question. (a) Show that the vertical component of the initial velocity of the javelin is 16.1ms -1. (b) Calculate the maximum height of the javelin above the ground. (4 marks)

25 (c) Athletes competing in a javelin throw try to achieve the maximum range. Describe and explain the effect that increasing the launch height of a javelin has on the maximum range.

26 QUESTION 15 A projectile is launched horizontally from a height of 2.4 m above ground level, with an initial velocity of magnitude V 0 = 65 ms -1. Ignore the effects of air resistance in parts (a) to (c) of this question. (a) State the magnitude of the horizontal component of the velocity of the projectile when it hits the ground. Justify your answer. (b) Show that the time of flight of the projectile is 0.70 s. (c) Calculate the range of the projectile.

27 (d) The photograph below shows four people playing badminton: During a badminton match a shuttlecock is hit at a height of 2.4 m above ground level. It then moves horizontally with an initial velocity of magnitude v 0 = 65 ms -1. Air resistance increases the time of flight of the shuttlecock to more than 0.70 s. Explain why air resistance increases the time of flight of the shuttlecock.