SOLUTION: A ski run must not exceed a slope of -3/5 due to safety concerns. What is the maximum elevation drop (in yards) if the run is to be 4000 yards long?

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Question 633441: A ski run must not exceed a slope of -3/5 due to safety concerns. What is the maximum elevation drop (in yards) if the run is to be 4000 yards long?
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A ski run must not exceed a slope of -3/5 due to safety concerns. What is the maximum elevation drop (in yards) if the run is to be 4000 yards long?
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Draw the picture.
You have a right triangle with
hypotenuse = 4000 yds.
slope = -3/5 = -0.6 yds
This means the skier decends 3 yds for each horizontal advance of 5 yds.
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Let vertical change be 3x; then horizontal change is 5x.
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(3x)^2 + (5x)^2 = 4000^2
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34x^2 = 4000^2
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x = sqrt[4000^2/34]
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x = 4000/sqrt(34)
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Total vertical change = 3x = 12000/sqrt(34) = 2058 yds
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Cheers,
Stan H.
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