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The Alert Hiker: An alert hiker sees a boulder fall from the top of a distant cliff and notes that it takes 1.3s for the boulder to fall the last third of the way to the ground.

a.What is the height of the cliff in meters?
b.If in part (a) you get two solutions of a quadratic equation and you use one for your answer, what does the other represent?

  • Physics -

    Let H be the height of the cliff. The the time required to fall a distance d is
    t = sqrt(2d/g)

    From the information given you can write:
    sqrt(2H/g) - sqrt[(2/3)*2H/g] = 1.3
    sqrt(2H/g)*[1 - sqrt(2/3)] = 1.3
    0.1835*sqrt(2H/g)= 1.3
    sqrt(2H/g) = 7.08
    H = 246 m
    Check: 2/3 of the way down is 164 m
    Time to fall 164 m = 5.785 s
    Time to fall 246 m = 7.085 s
    Difference = 1.30 s

    I did not have to solve a quadratic equation.

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