Question

A ball is dropped from a height of $10m$. If $40\%$ of its energy is lost on collision with the earth then after collision the ball will rebound to a height of

Answer 1

Given that the ball is dropped from a height, $h_1=10m$

Potential energy at $h_1=mg{h}_1$

Given $g=10m/s^2,h_1=10m$

Therefore the potential energy at $h_1=m\times 10\times 10$

$=100m$ J

On striking the ground level, the ball looses 40% of its initial energy:

i.e. $\left(\frac{40}{100}\right)\times 100m$ J

$=40m$ J

The energy left on striking the ground $=100m$ J - $40m$ J

$=60$m J

So the final energy of the ball , $mg{h}_2=60m$ J

i.e $h_2=\left(\frac{60}{10}\right)$

$=6m$

Hence the ball will bounce back to a height of $6m$