Question

A ball is projected vertically down with an initial velocity from a height of $15$ m on to a horizontal floor. During the impact it loses $25$% of its energy and rebounds to the same height, the initial velocity of its projections is

• A. $20m{s}^{-1}$
• B. $15m{s}^{-1}$
• C. $10m{s}^{-1}$
• D. $5m{s}^{-1}$

Answer 1

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

Let ball is projected vertically downward with velocity v from height h
Total energy at point $A=\frac{1}{2}m{v}^2+mgh$
During collision loss of energy is 50% and the ball rises up to same height. It means it possess only potential energy at same level.
$50$ % $(\frac{1}{2}mv62+mgh)=mgh$
$\frac{1}{2}(\frac{1}{2}m{v}^2+mgh)=mgh$
$v=\sqrt{2gh}=\sqrt{2\times 10\times 20}$
$\therefore v=20m/s$