A ball is dropped from a height h on to a floor . If the cofficient of restitution is e, calculate the height the ball first rebounds ?

Explanation

If a body falls from height h, from equations of motion we know that it will hit the ground with a velocity say `u =sqrt(2gh)` which is also the velocity of approach here.
Now if after collision it regains a height `h_(1)` then again by equations of motion v = `sqrt(2gh_(1))` which is also the velocity of separation. So, by definition of e.
`e=sqrt((2gh_(1))/(2gh))` or `h_(1)=e^(2)h`