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

The velocity of particle after falling through height h  u=2gh …(i) v2=u2−2gh∴ 0=e2u2−2gh1 or  h1=e2u22g=e22gh2=e2h[ From Eq. (i)] 0=e4u2−2gh2 or  h2=e4h            =h+2h1+2h2+…∞=h+2e2h+2e4h+…∞=h+2e2h1+e2+e4+…∞=h+2e2h11−e2=h1+2e21−e2=1+e21−e2h