A small ball of mass 0.2 kg is moving vertically downwards when it hits a horizontal floor. Immediately before hitting the floor the ball has speed \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Immediately after hitting the floor the ball rebounds vertically with speed \(7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
Find the magnitude of the impulse exerted by the floor on the ball.
By modelling the motion of the ball as that of a particle moving freely under gravity,
find the maximum height above the floor reached by the ball after it has rebounded from the floor,
find the time between the instant when the ball first hits the floor and the instant when the ball is first 1 m above the floor and moving upwards.