Question:
A ball of mass $m$ is dropped onto a floor from a certain height. The collision is perfectly elastic and the ball rebounds to the same height and again falls. Find the average force exerted by the ball on the floor during a long time interval.
Solution:
$v^{2}=2 g h \Rightarrow v=\sqrt{2 g h}$
$v^{\prime}=-\sqrt{2 g h}$
$F=\frac{m \Delta v}{\Delta t}=\frac{m 2 \sqrt{2 g h}}{\Delta t}$
For falling down,
Time taken $t_{1} \Rightarrow 0=+v+a t_{1}$
$\Rightarrow v=g t_{1} \quad\{a=-g\}$