# 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 below illustrates.The crest of the second hill is circular, with a radius of r = 33.3 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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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 below illustrates.

The crest of the second hill is circular, with a radius of r = 33.3 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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Step 1

Using conservation of energy,

Step 2

As  the skier just loses contact at the crest of the second hill, the weight equals the centripetal force. Therefore,

Step 3

Substituting the second equ...

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