A ball is thrown vertically downwards from a height of $\mathrm{20\; m}$ with an initial velocity $v_0$. It collides with the ground, loses $50$ percent of its energy in collision and rebounds to the same height. The initial velocity $v_0$ is: (Take $g=10\mathrm{ }\mathrm{m }{\mathrm{s}}^{-2}$)

• Correct answer
  A

  $20\mathrm{ }\mathrm{m }{\mathrm{s}}^{-1}$
• B

  $28\mathrm{ }\mathrm{m }{\mathrm{s}}^{-1}$
• C

  $10\mathrm{ }\mathrm{m }{\mathrm{s}}^{-1}$
• D

  $14\mathrm{ }\mathrm{m }{\mathrm{s}}^{-1}$

Solution

kinetic energy of the ball on reaching ground 

$K{E}_1=mgh+\frac{1}{2}m{v}_0^2$

after collision $\frac{K{E}_1}{2}=mgh$

$\frac{mgh+\frac{1}{2}m{v}_0^2}{2}=mgh$

$v_0=\sqrt{2gh}=20\text{m}{\text{s}}^{-1}$

Hence, the correct answer is option: 'A'.