A ball kept at $20 \mathrm{~m}$ height falls freely in vertically downward direction and hits the ground.…
A ball kept at $20 \mathrm{~m}$ height falls freely in vertically downward direction and hits the ground. The coefficient of restitution is $0.4$. Velocity of the ball first rebound is $\left[\mathrm{g}=10 \mathrm{~ms}^{-2}\right]$
$4 \mathrm{~ms}^{-1}$
$8 \mathrm{~ms}^{-1}$
$12 \mathrm{~ms}^{-1}$
$16 \mathrm{~ms}^{-1}$
Solution
$\begin{aligned}
v^2 & =0+2 g h \quad \ldots\left(\because v^2-u^2=2 g h\right) \\
& v^2=2 \times 10 \times 20=400 \\
& v=20 \mathrm{~m} / \mathrm{s} \\
& \mathrm{e}=\frac{\mathrm{u}}{\mathrm{v}}
\end{aligned}$
$\therefore \quad$ The velocity of the body after the first rebound is
$\begin{aligned}
& u=0.4 \times 20 \\
& u=8 \mathrm{~m} / \mathrm{s}
\end{aligned}$