Question

A ball falls under gravity from a height of $10m$ with an initial downward velocity $u$. If collides with the ground, losses $50$% of is energy in collision and then rises back to the same height. The initial velocity $u$ is:

• A. $7m{s}^{-1}$
• B. $25m{s}^{-1}$
• C. $14m{s}^{-1}$
• D. $28m{s}^{-1}$

Answer 1

The correct option is C $14m{s}^{-1}$

If $m$ is the mass of the ball, then its total initial energy at height $h$.
$=\frac{1}{2}m{u}^2+mgh$
Energy after collision $=50$% of $(\frac{1}{2}m{u}^2+mgh)$
$=\frac{1}{2}(\frac{1}{2}m{u}^2+mgh)$
As the ball rebounds to height $h$, so
$=\frac{1}{2}(\frac{1}{2}m{u}^2+mgh)=mgh$ or

$=\frac{1}{4}m{u}^2=\frac{1}{2}mgh$
$u=\sqrt{2gh}$

$u=\sqrt{2\times 9.8\times 10}=14m{s}^{-1}$.