4. A ball of mass 0.2 kg is projected vertically downwards with speed \(U \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a point A which is 2.5 m above horizontal ground. The ball hits the ground. Immediately after hitting the ground, the ball rebounds vertically with a speed of \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The ball receives an impulse of magnitude 7 Ns in its impact with the ground. By modelling the ball as a particle and ignoring air resistance, find

1. the value of \(U\). After hitting the ground, the ball moves vertically upwards and passes through a point \(B\) which is 1 m above the ground.
2. Find the time between the instant when the ball hits the ground and the instant when the ball first passes through \(B\).
3. Sketch a velocity-time graph for the motion of the ball from when it was projected from \(A\) to when it first passes through \(B\). (You need not make any further calculations to draw this sketch.)