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Question 1083705: A tennis ball is dropped from a height of 20 m and bounces to 40% of its previous height on each bounce. The total vertical distance travelled is made up of the upward bounces and downward drops. What is the total vertical distance the ball has travelled when it hits the floor for the 6th time?
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! The solution is to sum a geometric series
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The tennis ball is dropped from a height of 20 m. After it hits the floor, it reaches a height of 20 * 0.40 = 8 m
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After it hits the floor for the second time, it reaches a height of 8 * 0.40 = 3.2 m
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and so forth
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Note that after bouncing to a distance, it falls that same distance
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let d(n) be the distance the tennis ball has traveled when it hits the floor for the nth time, then
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d(1) = 20
d(2) = 20 + 2 * 20 * 0.40
d(3) = 20 + 2 * 20 * 0.40 + 2 * 20 *(0.40)^2
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therefore,
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d(n) = 20 + 2 * 20 * 0.40 + .... + 2 * 20 * (0.40)^(n-1)
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d(6) = 20 * ( 1 - 0.40^6) / ( 1 - 0.40) = 33.2 m
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the tennis ball travels 33.2 m after it hits the floor for the 6th time
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