Question

A particle falls from a height h on a fixed horizontal plate and rebounds. If e is the coefficient of restitution, the total distance travelled by the particle before it stops rebounding is

• A. $\frac{h(1+e^2)}{(1-e^2)}$
• B. $\frac{h(1-e^2)}{(1+e^2)}$
• C. $\frac{h(1-e^2)}{2(1+e^2)}$
• D. $\frac{h(1+e^2)}{2(1-e^2)}$

Answer 1

The correct option is A

$\frac{h(1+e^2)}{(1-e^2)}$

The total distance travelled is given by
$s=h+2e^{2}h+2e^{4}h+2e^{6}h+\dots \dots$
$=h+2h(e^2+e^4+e^6+\dots \dots )=h+2h\left(\frac{e^2}{1-e^2}\right)=h(1+\frac{2e^2}{1-e^2})=\frac{h(1+e^2)}{1-e^2}$
Hence, the correct choice is (a).