A hard ball dropped from a height of 1 m in earth’s gravitational field bounces to a height of 95 cm. What

Question

will be the total distance traversed by the ball?

Answer 1

Counting all bounces? That would be

100 (1 + 2*0.95 + 2*0.95^2 + 2*0.0.95^3 + ... centimeters. That is an infinite series, and assumes that the down-to-up ratio is always 0.95.

That can be written as

100*(2 + 2*0.95 + 2*0.95^2 + 2*0.0.95^3....) - 100

or, in closed form, as

200[1/(1-0.95)] - 100
= 3900 cm

Answer 2

A question like this was answered recently. I'll try to find a link.

Answer 3

drwls is faster than me!!