# A rubber ball is made to fall from a height of 50 feet and is observed to rebound 2/3 of the distance it falls . how far will the ball travel before carrying the rest if the ball continues to fall in this manner

1
by johnirinco123

2014-11-20T22:51:40+08:00
See attachment for illustration
Let a1 be 2/3(50) = 100/3
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Since this is in infinite geometric progression then we'll use

where r is the common ratio

Since the distance traveled by the ball is twice 2/3 of the previous then we'll have Sn multiplied by 2

But remember that we have not included the initial 50ft distance traveled since a1 is 2/3 of 50.
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Total distance traveled by the ball then is