Question

A tennis ball is dropped from the height h above the ground. If the ball strikes to the ground elastically, what height will the ball achieve after the first collision?
(correct answer + 1, wrong answer - 0.25)

• A. $h{e}^6$
• B. $e^{2}h$
• C. $e^{3}h$
• D. None of these

Answer 1

The correct option is B $e^{2}h$

Given,
Initial height $=h$
$v_{\text{final}}=\text{final velocity}$
$v_{\text{initial}}=\text{initial velocity}$
Coefficient of elasticity = the square root of the ratio of the kinetic energy after and before the collision.
$e=\frac{v_{\text{final}}}{v_{\text{initial}}}=\sqrt{\frac{K_{\text{final}}}{K_{\text{initial}}}}=\sqrt{\frac{K_1}{K_0}}$
$K_1=e^2{K}_0$
$mg{h}_1=e^{2}mgh$
$h_1=e^{2}h$
Hence, the height after first collision is $e^{2}h$.