Question

After falling from a height $h$ and striking the ground twice, a ball rise up to the height [$e=$ coefficient of restitution] :

• A. $he$
• B. $h{e}^2$
• C. $h{e}^3$
• D. $h{e}^4$

Answer 1

The correct option is D $h{e}^4$

Coefficient of restitution is $e=\frac{v_1}{v_2}$, $v_1$ is raising velocity and $v_2$ is falling velocity.

$⟹K{E}_f=\frac{1}{2}m{v}_2^2=\frac{1}{2}m(v_{1}e{)}^2$

By conservation of energy, $mg{h}_f=\frac{1}{2}m(v_{1}e{)}^2=mgh{e}^2$

Hence after two collisions $h_f=h{e}^4$