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?

Answer 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