Bouncing ball elastic collision

[anand]

A ball drops to the floor and bounces,eventually coming to rest.Collisions between the ball and floor are elastic;the speed after each collision is e times the speed before collision where e<1.If speed just before 1st bounce is v,find the time taken to come to rest.

 

[Hootenanny]

Do you have any thoughts on the question yourself? Could I also ask that in future you would post homework questions using the template provided.

 

[anand]

Here is how I thought of doing it.
Use impulse=change in momentum
for successive bounces and add them all up(infinite series).Assume the force F to be a constant,so that it can be taken out of the integral sign.To find force F,use
work=change in kinetic energy.
The distance traveled by the ball can be found as sum of an infinite series.
Substituting the value of F,time can be found.
Is this approach correct?