A ball is thrown vertically upwards towards a ceiling and then rebounds, as illustrated in Fig. 3.1. [Figure 3.1] The ball is thrown with speed 9.6 m s⁻¹ and takes a time of 0.37 s to reach the ceiling. The ball is then in contact with the ceiling for a further time of 0.085 s until leaving it with a speed of 3.8 m s⁻¹. The mass of the ball is 0.056 kg. Assume that air resistance is negligible.

1. (a)Show that the ball reaches the ceiling with a speed of 6.0 m s⁻¹.[1]
2. (b)Calculate the height of the ceiling above the point from which the ball was thrown. height = ........................................................................................... m[2]
3. (c)Calculate
4. (c)(i)the increase in gravitational potential energy of the ball for its movement from its initial position to the ceiling,[2]
5. (c)(ii)the decrease in kinetic energy of the ball while it is in contact with the ceiling.[2]
6. (d)State how Newton's third law applies to the collision between the ball and the ceiling.[2]
7. (e)Calculate the change in momentum of the ball during the collision. change in momentum = ......................................................................... N s[2]
8. (f)Determine the magnitude of the average force exerted by the ceiling on the ball during the collision. average force = ................................................................................... N[2]

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