Question

A body falls from a height h on a horizontal surface and rebounds. Then it falls again and rebounds and so on. If the restitution coefficient is $\frac{1}{3}$, the total distance covered by the body before it comes to rest is

• A. $\frac{h}{4}$
• B. $\frac{5h}{4}$
• C. $2h$
• D. $3h$

Answer 1

The correct option is B

$\frac{5h}{4}$

Total distance travelled is given by $s=h+2e^{2}h+2e^{4}h+\dots \dots$
$=h+2e^{2}h(1+e^2+e^4+\dots \dots )=h+\frac{2e^{2}h}{1-e^2}=h\left(\frac{1+e^2}{1-e^2}\right)=h\left[\frac{1+{\left(\frac{1}{3}\right)}^2}{1-{\left(\frac{1}{3}\right)}^2}\right]=\frac{5h}{4}$
Hence, the correct choice is (b).