Solve the following :

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:

$v=\sqrt{2 g h}=\sqrt{2 \times 9.8 \times 2}$

$v_{1}+e v=0$

$v_{1}=-\sqrt{2 \times 9.8 \times 1.5}$

$e=\frac{-v_{1}}{v}$

$=\frac{+\sqrt{2 \times 9.8 \times 1.5}}{\sqrt{2 \times 9.8 \times 2}}$

$=\frac{\sqrt{3}}{2}$

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