Question

A particle falls from a height 'h upon a fixed horizontal plane and rebounds. If 'e' is the coefficient of restitution, then the total distance travelled before rebounding has stopped is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Particle falls from height h then formula for height covered by it in nth rebound is given by $h_n=h{e}^{2n}$

where e = coefficient of restitution, n = No. of rebound

Total distance travelled by particle before rebounding has stopped

$H=h+2h_1+2h_2+2h_3+2h_n+\cdots \cdots =h+2h{e}^2+2h{e}^4+2h{e}^6+2h{e}^8+\cdots \cdots =h+2h(e^2+e^4+e^6+e^8+\cdots \cdots )=h+2h\left[\frac{e^2}{1-e^2}\right]=h[1+\frac{2e^2}{1-e^2}]=h\left(\frac{1+e^2}{1-e^2}\right)$