A ball is dropped onto a fixed horizontal surface from height h0. The coefficient of restitution is e. Find the total distance D travelled by the ball before it comes to rest on the surface.
h0(1+e2)(1−e2)
Let hi(I=1,2,3,⋯⋯.) be the height of rebound after the ith impact.
Then e=hihi−1 which gives hn=e2nh0 (n=1.2.3⋯⋯⋯.)
D=h0+2( h1+h2+h3+h4+h5+⋯⋯)
=h0{10+2(e2+e4+e6+e8+e10+⋯⋯⋯)}D=h0(1+e21−e2)