Question

If a body falls normally on a surface from height h what will be the height regained after collision if coefficient of restitution is e

Answer 1

If the body falls a height h, the velocity it'll acquire will be:

$v_{i} = \sqrt{2gh}$

Now, according to the coefficient of restitution:

$e = \frac{v_{f}}{v_{i}}$

So, $v_{f} = ev_{i}$

Finally, the height it will reach shall be equal to:

$h_{f} = \frac{v_{f}^2}{2g}$

Which is equal to:

$h_{f} = \frac{e^2 * 2gh}{2g}$

Hence,

$h_{f} = e^2h$