Question

A ball is thrown vertically downwards from a height of 20m 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:

• A. 28 m/s
• B. 10 m/s
• C. 14 m/s
• D. 20 m/s

Answer 1

The correct option is D

20 m/s

When it hits the ground

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

It loses 50% energy, it left with 50% energy, this left energy converted into potential energy

$\frac{50}{100}[\frac{1}{2}m{v}_0^2+mgh]=mghm\frac{v_0^2}{2}+mgh=2mghm{v}_0^2+2mgh=4mgh{v}_0^2=2gh{v}_0^2=2\times 10\times 20v_0^2=400v_0=20m/s$