Question:
A ball falls on the ground from a height of $2.0 \mathrm{~m}$ and rebounds up to a height of $1.5 \mathrm{~m}$. Find the coefficient of restitution.
Solution:
$v=\sqrt{2 g h}=\sqrt{2 \times 9.8 \times 2}$
$v_{1}+e v=0$
$v_{1}=-\sqrt{2 \times 9.8 \times 1.5}$
$e=\frac{-v_{1}}{v}$
$=\frac{+\sqrt{2 \times 9.8 \times 1.5}}{\sqrt{2 \times 9.8 \times 2}}$
$=\frac{\sqrt{3}}{2}$