Calculating Time and Speed of Rebounds with Coefficient of Restitution

[Darth Vader]

Homework Statement

I drop a ball downwards vertically onto a smooth table. The coefficient of restitution is 0<e<1. The ball rebounds upwards vertically with speed x. What is the time taken between the time that the ball was dropped to its nth rebound?

Also, what is the time taken before the ball becomes stationary?

Homework Equations

e = speed of separation/speed of approach
Constant acceleration formulae

The Attempt at a Solution

Say the ball rises to a height h after the first rebound. Then h = x^2/(2g). The time taken to reach this height is t = x/g using the quadratic formula...

 

[haruspex]

Say the ball rises to a height h after the first rebound. Then h = x^2/(2g).

Yes.

The time taken to reach this height is t = x/g using the quadratic formula...

That cannot be right because the right hand side has dimension time-squared.

With what speed does it hit the floor the second time? What will be the next rebound speed?