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.
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)
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? (5 marks)
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 (1 mark) (3) Explain how we can use the diagram to deduce that the velocity of ball A increases during its fall.
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 (b) the velocity of the parcel after two seconds (3) Explain what happens to the two components of the velocity of the parcel as it falls to the water. (4 marks)
(4) What time, from the moment that it is released, does it take for the parcel to hit the water. (5) Determine the maximum horizontal distance achieved by the projectile
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. (4 marks) (3) What is the velocity of the projectile at point X?
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. (5 marks)
QUESTION 8 A mortar shell is fired from ground level (at point A on the diagram) with a velocity v 0 = 100 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.
(3) Calculate the resultant velocity of the shell after 13 seconds. (5 marks) (4) What is the velocity of the shell at point B? (1 mark) (5) What is the magnitude and direction of the acceleration of the shell at point B? (6) Determine the maximum height achieved by the shell. (3 marks)
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? 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) How long does it take before the stone hits the water? (3) What is the vertical velocity of the stone on impact with the water?
(4) What is the velocity of the stone on impact with the water? (5) How far does the stone travel horizontally from the point of projection before it hits the water? (5 marks)
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 44 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. (5 marks)
QUESTION 11 Water leaves a hose at a speed of V 0 = 2.0 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. (c) What will be the effect on the range if the angle between the nozzle and the horizontal is slightly decreased? Explain your answer. (2marks)
(2) (a) Find the maximum height of the water above ground level. (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. (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. (2marks)
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. (3 marks) (3) What is the initial vertical velocity of the cannonball? (1 mark) (4) What is the speed of the cannonball at the top of its flight path? (1 mark)
(5) Find the time taken for the cannonball to reach its maximum height. (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.
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. (3 marks) (2) the horizontal component of the ball's initial velocity. (3 marks) (3) the range of the ball.
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. (8 marks)
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;