A body falls freely from height ‘h’. If the coefficient of restitution is e, then calculate the height achieved after one bounce.

When a body falls from height h, it strikes the ground with a velocity $\mathrm{v}=\sqrt{2\mathrm{gh}}$

 Let it rebounce with a velocity v and rise to a weight ${\mathrm{h}}_1\text{. }$

$$\begin{gathered} \mathrm{v}=\sqrt{2{\mathrm{gh}}_1} \\ e=\frac{\mathrm{u}}{\mathrm{v}}\sqrt{\frac{{\mathrm{h}}_1}{\mathrm{h}}} \\ \text{ Clearly, }{\mathrm{h}}_1={\mathrm{e}}^2\mathrm{h} \end{gathered}$$