QUESTION 1. Sketch graphs (on the axes below) to show: (1) the horizontal speed v x of the ball versus time, for the duration of its flight;

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1 QUESTION 1 A ball is thrown horizontally from a cliff with a speed of 10 ms -1 shown in the diagram at right. Neglecting the effect of air resistance and taking gravitational acceleration to be g +9.8ms -2, Sketch graphs (on the axes below) to show: (1) the horizontal speed v x of the ball versus time, for the duration of its flight; (2) the vertical velocity v y of the ball versus time, for the duration of its flight. (4 marks) On the same axes, sketch graphs to show the horizontal speed and the vertical velocity versus time if air resistance has a significant effect on the flight of the ball. Label each graph clearly to distinguish it from the previous graph.

2 QUESTION 2 On each of the two projectile trajectories depicted below, draw vectors to show the directions and relative magnitudes of the velocity and the acceleration of the projectile at each of the points A, B & C. (3 marks) (3 marks)

3 QUESTION 3 A tennis player hits a ball horizontally at 35 ms -1 when it is 1.6 m above the ground. (a) How long is it before the ball hits the ground?,... (b) If the ball is hit 11.0 m from the net, will the ball clear the net which is 0.90 m high? If the ball is launched at a height of 1.6 m above the ground and the net is 0.90 m above the ground, we are trying to calculate the horizontal distance the ball will travel in this time at a height of 0.70 m.,... The horizontal range covered by the projectile in this time is: (3 marks).. (.) The net is 11.0 m away. The ball will travel 13.3 m. The ball will clear the net!

4 QUESTION 4 The multiple image photograph on the right shows the motion of two balls that are released at the same time from the same height above the surface. Ball A falls freely while ball B is projected horizontally. (1) Draw and label the horizontal component of velocity for the ball on the right (2) Explain why both balls will still hit the ground at the same time in spite of one covering a greater horizontal distance Both ball are released from the same height above the ground (S v ). Each is affected by the same acceleration due to gravity (g). (1 mark) Given the formula: $, if these variables are the same for both balls, the balls will fall with the same period and therefore hit the ground at the same time (3) Explain how we can use the diagram to deduce that the velocity of ball A increases during its fall. By measuring the distance between consecutive images, it is possible to show that the vertical distance between each image is increasing. If this distance is (1 mark) increasing, so too is the magnitude of the vertical velocity

5 QUESTION 5 A parcel is to be dropped from an aeroplane to a boat at sea. The aeroplane is flying with a speed of 100 ms -1 at a fixed altitude of 120 m above sea level. (1) Calculate the vertical distance that the parcel has fallen in the first two seconds..(.). (2) Calculate: (a) the vertical velocity of the parcel after two seconds v u + at v (2) v 19.6 ms -1 down (b) the velocity of the parcel after two seconds 100 ms -1 % & '. %. ( ). ) % 19.6 ms -1 ). *+, +-+ (4 marks) (3) Explain what happens to the two components of the velocity of the parcel as it falls to the water. The horizontal velocity stays constant as there is no force horizontally. The vertical velocity will increase as the force of gravity acts vertically.

6 (4) What time, from the moment that it is released, does it take for the parcel to hit the water., rearranges to give: $... (5) Determine the maximum horizontal distance achieved by the projectile... (.)

7 QUESTION 6 At a point on the upward path of a projectile the velocity of the projectile is 18 ms -1 at 40 above the horizontal, as shown in the diagram. (1) Find the horizontal and vertical components of the velocity at this point. +). +. )... (. ( (4 marks) (2) Describe how (and explain why) these components of velocity will change over the rest of the flight. V H will not change as there is no force horizontally. V v will change continuously due to the downwards force of gravity. (4 marks) (3) What is the velocity of the projectile at point X? At X, velocity is 13.8 ms -1 as the V v is zero at X.

8 QUESTION 7 A gun, aimed horizontally, fires a bullet with a speed of 900 ms -1. The gun is 2.0 m above ground level. The time of flight of the bullet is 0.64s. (1) Find the range of the bullet... (.) (2) Find the velocity with which the bullet hits the ground. ' '.... (, down 900 ms -1 % 6.27 ms -1 % & '. %. ( (4 marks)

9 QUESTION 8 A mortar shell is fired from ground level (at point A on the diagram) with a velocity V ms -1 at an angle of 80 above the horizontal. (1) Calculate the horizontal and vertical components of the velocity of the shell at the instant it is fired. +) + ).. (. ( (4 marks) (2) Calculate the vertical component of the velocity: (i) one second after firing '.'(.).. ( (ii) thirteen seconds after firing. '.'(.).. ( (. (,0+,)

10 (3) Calculate the resultant velocity of the shell after 13 seconds. % &.. '. %. ( )..... ) *+, +-+ ) % 17.4 ms ms -1 (4 marks) (4) What is the velocity of the shell at point B? V H horizontally 17.4 ms -1 horizontal (1 mark) (5) What is the magnitude and direction of the acceleration of the shell at point B? a g 9.8 ms -2 down (6) Determine the maximum height achieved by the shell. Maximum height v 2 u 2 + 2as 0 (98.5) 2 + 2(-9.8)s s 495m (3 marks)

11 QUESTION 9 (1) If a body is dropped from a height of 40 m and falls freely, how long does it take before it hits the ground?, rearranges to give: $... A stone of mass 200 g is thrown with a velocity of V 0 30 ms -1 horizontally from the observation deck of a lighthouse. At the moment of release the stone is 40 m above sea level. (2) What is the vertical velocity of the stone on impact with the water? V V 0 + at V (2.86) V 28.0 ms -1

12 (4) What is the velocity of the stone on impact with the water? % &. '. %.. ( ).... ). *+, +-+ ) % 30.0 ms ms -1 (4 marks) (5) How far does the stone travel horizontally from the point of projection before it hits the water?.. (.)

13 QUESTION 10 A golfer hits a ball from an elevated tee, at a height of 20 m above the green. The ball is hit with a velocity of 50 ms -1 at an angle of 20 to the horizontal. The time of flight of the ball is 4.4 s. (1) Find the horizontal and vertical components of the initial velocity. +) + ).. (. ( (4 marks) (2) Find the distance that the ball travels horizontally before it hits the green (.) (3) Find the velocity of the ball when it hits the green. Vertical velocity on impact V V 0 + at 47.0 ms -1 V (-9.8) (4.4) V 26.0 ms -1 ) % 26.0 ms -1 % &.. '. %. ( (4 marks) ).... ) *+, +-+

14 QUESTION 11 Water leaves a hose at a speed of V ms -1, at an angle of 45 above the horizontal. The nozzle is 1.2m above ground level. The time of flight of a water droplet is 2.96s. (1) (a) Determine the horizontal distance from the nozzle to the point where the water hits the ground. (. +.)... (.) (b) What will be the effect on the range if the angle between the nozzle and the horizontal is slightly increased? Explain your answer. The range will be reduced As the angle increases, the magnitude of the horizontal velocity decreases. The horizontal velocity is directly proportional to the range. As the horizontal velocity decreases, the range will decrease proportionally (c) What will be the effect on the range if the angle between the nozzle and the horizontal is slightly decreased? Explain your answer. As the angle decreases, the magnitude of the horizontal velocity increases. The horizontal velocity is directly proportional to the range. As the horizontal velocity increases, the range will increase proportionally (2marks)

15 (2) (a) Find the maximum height of the water above ground level. v 2 u 2 + 2as 0 (2.0 x sin45 ) 2 + 2(-9.8)s 1 ( ) m above ground level m (3 marks) (b) What will be the effect on the maximum height if the angle between the nozzle and the horizontal is slightly increased? Explain your answer. The maximum height will be increased if the angle is increased. This is because the vertical component of the initial velocity will increase. Vertical component of velocity is directly proportional to max. height. (c) What will be the effect on the maximum height if the angle between the nozzle and the horizontal is slightly decreased? Explain your answer. The maximum height will be decreased if the angle is decreased. This is because the vertical component of the initial velocity will decrease. (2marks) Vertical component of velocity is directly proportional to max. height.

16 QUESTION 12 A cannonball is fired at an angle of 45 to the horizontal, thus achieving its maximum range of 290 m on horizontal ground. The cannon ball has a flight time of 7.693s. Assume that the cannonball is projected from ground level. (1) Find the horizontal component of the velocity of the cannon-ball during its flight ( (2) Find the initial velocity of the cannonball. V H V cos 45 V 37.7 cos 45 V 53.3 ms -1 (3 marks) (3) What is the initial vertical velocity of the cannonball? 37.7 ms -1 (1 mark) (4) What is the speed of the cannonball at the top of its flight path? 37.7 ms -1, horizontal (to the right) (1 mark)

17 (5) Find the time taken for the cannonball to reach its maximum height. Maximum height at half the time of flight s (3 marks) (6) In another identical firing of this cannon, the cannonball encounters a horizontal headwind (i.e. there is no effect on its vertical velocity, only the horizontal speed is reduced). Explain what effect this wind will have on (i) the time of flight and (ii) the range of the cannonball. (i) No effect on the time of flight as it is dependent on the vertical component of velocity. (v u + at) (ii) The range will be reduced. Range V H x t R V H reduce V H, reduce range.

18 QUESTION 13 In an investigation into projectile motion, students projected a golf ball from ground level with the same initial speed but at different angles to the horizontal. At their first attempt the ball was projected at 45 to the horizontal and the range was noted. In subsequent attempts, the angle of projection was progressively increased. Explain what effect (if any) increasing the angle of projection has on: (1) the ball's time of flight. The time of flight t is given by 8 9(: ;, where V v V 134< Substitution gives < (: ; This shows that t 134< If we increase <, 134< increases (3 marks) If 134< increases, the time of flight increases. (2) the horizontal component of the ball's initial velocity. V H 9 >1< if we increase <, >1< decreases Thus V H decreases proportionally (3 marks) (3) the range of the ball. The range will decrease as V H decreases 45 gives the maximum range.

19 QUESTION 14 An athlete, competing in a shot put event, throws a shot of mass 60 kg with an initial speed of 13 ms -1 at an angle of 40 to the horizontal. Calculate the horizontal distance that the shot travels and its velocity when it hits the ground if it leaves the athlete's hand at a height of 2.0 m above ground level. The time of flight of the shot is 1.9 s. +) +. ).. (. (... (.) Vertical velocity on impact V V 0 + at V (-9.8)(1.9) V ms -1 % &. '. %.. ( )... ) *+, ms -1 ) % 13.0 ms -1

20 QUESTION 15 Two baseball players are throwing a ball to each other as shown at right. The ball is released and caught at the same height above ground level. Taking the upward direction to be positive, on the axes below, sketch graphs of the following (a) the horizontal velocity of the ball whilst in flight; (b) the acceleration of the ball whist in flight;