6 A small ball of mass 0.5 kg is held at a height of 3.136 m above a horizontal floor. The ball is released from rest and rebounds from the floor. The coefficient of restitution between the ball and floor is \(e\).
- Find in terms of \(e\) the speed of the ball immediately after the impact with the floor and the impulse that the floor exerts on the ball.
The ball continues to bounce until it eventually comes to rest.
- Show that the time between the first bounce and the second bounce is \(1.6 e\).
- Write down, in terms of \(e\), the time between
(a) the second bounce and the third bounce,
(b) the third bounce and the fourth bounce. - Given that the time from the ball being released until it comes to rest is 5 s , find the value of \(e\).