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A ball is dropped from a height of 6 feet and begins bouncing. The height of each bounce is three-fourths the height of the previous bounce. Find the total vertical distance the ball travels before coming
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A ball is dropped from a height of 6 feet and begins bouncing. The height of each bounce is three-fourths the height of the previous bounce. Find the total vertical distance the ball travels before coming to rest?

User Nojo
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6 votes
theoretically, the answer is infinity. however, in a non perfect universe such as our own, practically the answer would be around 17ft.
User Paul Reznik
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The sum to infinity of a geometric sequence where the first term is a and the common ratio r is less than 1 is:

S_(\infty) =(a)/(1-r)
Using this formula, the total vertical distance the ball travels before coming to rest is given by:

S_(\infty)=(6)/(1-(3)/(4))=24\ feet
User Davidmytton
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