Question

A ball is dropped from a height of $H$. The ball bounces on the ground and jumps back up to a height of $h$. If the ball lost $x$ times its own energy, then what is the value of $h$ in terms of $x$ and $H$?

• A. $Hx$
• B. $H(1-x)$
• C. $\frac{H}{x}$
• D. $\frac{H}{1-x}$

Answer 1

The correct option is B $H(1-x)$

Given:
Height of the ball before drop $=H$
Height of the ball after bounce $=h$
Energy loss $=x$

Assume:
Initial energy of the ball $=E$
Weight of the ball $=mg$

Energy of the ball initially,
$E=mg\times H$ ------ (1)
Energy is conserved during the fall
$⟹$Energy of ball just before hitting the ground $=E$
Energy lost after bounce $=xE$
Energy of ball just after hitting the ground $=E-xE=E(1-x)$

Again, energy is conserved when the ball is bouncing back up.
Energy of ball reaching the top most point after bounce $=E(1-x)=mg\times h$ ------ (2)

Substituting (1) in (2):
$mgH(1-x)=mgh$
$⟹H(1-x)=h$