a skier sarts fro rest at the top of a hill. the skier coasts down the hill and

Question

a skier sarts fro 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 r = 36 m. Neglect friction and air resistance. What must be the height h of the first hill so that the skier just loses contactt with the snow atthe snow at the crest of the second hill? ( hint: Here you may want to use both energy conservation and force methods as part of your solution. in any case you should identify what forces would be direct radially inwards when the skier is at the crest of the second hill and remember that these are the forces that would generate the skier's centripetal acceleration. of these forces, which would vanish if contact between the skier and the hill was los? this force might then be set to zero in the solution.)

Explanation / Answer

radius of the crest of the second hill r = 36m

accleration g = 9.8m/s^2

the skier will lose contact if the velocity at the second hill is v

mg = mv^2/r

    v =18.73m/s

from the law of conservation of energy

mgh = 1/2 * mv^2

h = ( 18.783m/s)^2/19.6m

h = 18m

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