Question

A ball, when dropped, will bounce \dfrac{1}{3} 3 1 of the height from which it was dropped. If the ball is dropped from 54 feet, what is the total distance in feet the ball will have traveled the moment it hits the ground for the third time?

Answer 1

so its not elastic collision.

to calculate the total distance traversed by the ball up to the third bounce

one has to take the instant up to the 3rd hit.

if the distance is

D = h(0) + (3/4). h(0) + (3/4) h(0) + (3/4).(3/4) h(0) + (3/4).(3/4) h(0)

this distance = down + up +down +up +down only

otherwise it will do the after 3rd bounce travel.

D = h(0) { 1 + 2. (3/4) + 2. (9/16) }

= 3.625 h(0)