A ball is dropped from a height of 3 ft. The elasticity of the ball is such that it always bounces up one-third the distance it has fallen.
(a) Find the total distance the ball has traveled at the instant it hits the ground the fourth time. (Enter your answer as an improper fraction.) Can someone show me how to do this?

Question

A ball is dropped from a height of 3 ft. The elasticity of the ball is such that it always bounces up one-third the distance it has fallen.
(a) Find the total distance the ball has traveled at the instant it hits the ground the fourth time. (Enter your answer as an improper fraction.)     Can someone show me how to do this?

anonymous · Answer

Think of this one in steps.
First it falls 3ft to reach the ground. Then bounces up 1/3 of that which is 1 ft.
It falls another 1ft back to the ground. Then bounces up 1/3 of that which is 1/3ft.

So add up all the distances it has traveled like that until it falls to the ground the fourth time.

anonymous · Answer

It is also a geometric series.

anonymous · Answer

I think the formula is a^n=5n but im not sure...

anonymous · Answer

i mean 3n