Question

A tennis ball is dropped from a height of 7 ft. If the ball rebounds 2/3 of its height on each bounce, how far will the ball travel before coming to rest? (Find the total distance that the ball will travel before it stops bouncing.)
i need help i don't know which formula to use to solve this problem.

Answers

in theory, the ball will never come to rest, since its bounce height is never zero.

But, you can see the height of the nth bounce is 7(2/3)^n

So, since the distance traveled is both up and down, the sequence is

7 + 2*7(2/3) + 2*7(2/3)^2 + ...
so, if r=2/3,
= 7 + 14(r+r^2+...)
After n bounces the sum is
7 + 14((1-r^n)/(1-r) - 1)
and as n->infinity, that leaves
7 + 14(3/2 - 1) = 7+7 = 14

I think ...

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