A ball is thrown vertically downwards to the ground, as illustrated in Fig. 2.1. ball speed u path of ball 1.5m speed 8.7 ms⁻¹ ground Fig. 2.1 The ball is thrown with speed u from a height of 1.5m. The ball then hits the ground with speed 8.7ms⁻¹. Assume that air resistance is negligible.

1. (a)Calculate speed u.[2]
2. (b)State how Newton's third law applies to the collision between the ball and the ground.[2]
3. (c)(i)The ball is in contact with the ground for a time of 0.091 s. The ball rebounds vertically and leaves the ground with speed 5.4ms⁻¹. The mass of the ball is 0.059 kg. Calculate the magnitude of the change in momentum of the ball during the collision.[2]
4. (c)(ii)Determine the magnitude of the average resultant force that acts on the ball during the collision.[1]
5. (c)(iii)Use your answer in (c)(ii) to calculate the magnitude of the average force exerted by the ground on the ball during the collision.[2]
6. (d)The ball was thrown downwards at time t = 0 and hits the ground at time t = T. On Fig. 2.2, sketch a graph to show the variation of the speed of the ball with time t from t = 0 to t = T. Numerical values are not required. speed 0 0 T t Fig. 2.2[1]
7. (e)In practice, air resistance is not negligible. State and explain the variation, if any, with time t of the gradient of the graph in (d) when air resistance is not negligible.[2]

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