Skier at the top of a hill

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A skier starts from rest at the top of a hill and coasts down to a second hill with a circular crest of radius 38.5m. To determine the height of the first hill where the skier just loses contact at the crest, energy conservation principles are applied, equating potential energy and kinetic energy. The correct relationship is established as mgh = 1/2 mv^2, leading to the conclusion that h must equal 1/2r. The initial calculation of 96.25m was incorrect, prompting a reevaluation of the height formula. The final determination is that the height h should be calculated as half the radius of the second hill.
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Homework Statement

A skier starts from rest at the top of a hill. The skier coasts down the hill and up a second hill,The crest of the second hill is circular, with a radius of r = 38.5m. 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?

Homework Equations

ke=1/2mv^2 and pe=mgh
e=pe+ke


The Attempt at a Solution

e=0 so pe =ke and h=(H-2r) and v^2=gr
so i found h=2r+r/2 and i got 96.25 m but its not right please help
 
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ok wait i think i found my problem it should be mgh=1/2mgr so h=1/2r...
 
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