Question

A tennis ball bounces down a flight of stairs, striking each step in turn and rebounding to the half of height of the step. The coefficient of restitution is

• A. $\frac{1}{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. $(\frac{1}{\sqrt{2}}{)}^{\frac{1}{2}}$
• D. $(\frac{1}{\sqrt{2}}{)}^{\frac{1}{4}}$

Answer 1

Answer: (B)

$\frac{1}{\sqrt{2}}$

Coefficient of restitution=$e=\frac{v_{sep}}{v_{app}}$

For each flight, the conservation of energy holds between points of hitting the ground and the point of maximum elevation.

$⟹\frac{1}{2}m{v}_{app}^2=mgh$

and $\frac{1}{2}{v}_{sep}^2=mg\frac{h}{2}$

$⟹\frac{v_{sep}}{v_{app}}=\frac{1}{\sqrt{2}}$

$⟹e=\frac{1}{\sqrt{2}}$