5 A ball is dropped from a height of 2.5 m above a horizontal floor. The ball bounces repeatedly on the floor.
- Find the speed of the ball when it first hits the floor.
- The coefficient of restitution between the ball and the floor is \(e\).
- Show that the time taken between the first contact of the ball with the floor and the second contact of the ball with the floor is \(\frac { 10 e } { 7 }\) seconds.
- Find, in terms of \(e\), the time taken between the second contact and the third contact of the ball with the floor.
- Find, in terms of \(e\), the total vertical distance travelled by the ball from when it is dropped until its third contact with the floor.
- State a modelling assumption for answering this question, other than the ball being a particle.