Question

A ball is thrown vertically downwards from a height of $20m$ with an initial velocity ${\upsilon }_0$. It collides with the ground, loses $50$ percent of its energy in collision and rebounds to the same height. The initial velocity ${\upsilon }_0$ is (Take $g=10m{s}^{-2}$)

• A. $10m{s}^{-1}$
• B. $14m{s}^{-1}$
• C. $20m{s}^{-1}$
• D. $28m{s}^{-1}$

Answer 1

The correct option is C $20m{s}^{-1}$

Initial energy $E_i=P.E.+K.E.=mgh+\frac{1}{2}m{v}_0^2$
Energy when it reaches the ground $E=\frac{1}{2}m{v}^{\prime 2}$ (since P.E. is zero)
Given, $E_f=\frac{1}{2}{E}_i$
Since it rises to the same height, $E_f=mgh+0$, is the final energy
$\Rightarrow \frac{1}{2}(mgh+\frac{1}{2}m{v}_0^2)=E_f=mgh+0$
$v^2=2gh=2\times 10\times 20={20}^2$
$\Rightarrow v=20m/s$