A ball is thrown vertically upward to a height of 45 feet. Each time the ball strike the ground, its rebound is 4/5 of the previous height. How far has the ball travelled when it strikes the ground the sixth time?
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A ball is thrown vertically upward to a height of 45 feet. Each time the ball strike the ground, its rebound is 4/5 of the previous height. How far has the ball travelled when it strikes the ground the sixth time?
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The scenario painted in the question can be modeled as a geometric series with an initial height (term) and common ratio of
. We are to find the sixth term.
The sum of the first 6 terms of a geometric sequence is given by
, where
is the first term and
is the common ratio.
Thus,
Now, we take notice that for each height, there is a rise and there is a fall. Thus, for each height, there the ball travels twice the height.
Therefore, the total distance traveled by the ball by the time it hits the ground the sixth time is
feet.