physics

A skier starts from rest at the top of a hill. The skier coasts down the hill and up a second hill, as the drawing illustrates. The crest of the second hill is circular, with a radius of 39.6 m. Neglect friction and air resistance. What must be the height h of the first hill so that the skier just loses contact with the snow at the crest of the second hill?

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  1. The speed V at the crest of the second hill must satisfy

    V^2/R = g
    where g = 9.8 m/s^2 and R = 39.6 m
    V = 19.7 m/s

    Use conservation of energy to get the required hill height H, measured above the crest of the second hill.

    g*H = V^2/2

    H = 19.8 m

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