A skater starts from rest at the top of a hill and moves up a second hill, as th

Question

A skater starts from rest at the top of a hill and moves up a second hill, as the drawing illustrates. The crest of the second hill is circular, with a radius r. Which of the following express the height of the first hill (h) so that the skater just loses contact at the crest of the second hill. Neglect friction and air resistance.

A skater starts from rest at the top of a hill and moves up a second hill, as the drawing illustrates. The crest of the second hill is circular, with a radius r. Which of the following express the height of the first hill (h) so that the skater just loses contact at the crest of the second hill. Neglect friction and air resistance.

Explanation / Answer

The normal force is zero, therefore:

v^2/r = g

==> v = sqrt(r g)

conservation of energy:

0.5 m v^2 = m g h

==> h = 0.5 v^2/g = (0.5 r g)/g = r/2

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