Solving the Physics of a Skier Leaving a Hill

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To determine when a skier leaves a hemispherical hill, the key concept is the point at which the normal force becomes zero. This occurs when the centripetal force required for the skier's circular motion is equal to the gravitational force acting on them. By applying conservation of energy principles and analyzing the forces at play, it can be shown that the skier will become airborne at a height of h = R/3 below the top of the hill, where R is the radius of the hill. Understanding these dynamics is crucial for solving the problem effectively. The discussion emphasizes the importance of balancing forces and energy conservation in this physics scenario.
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Homework Statement


A skier starts from rest at the top of a large hemispherical hill. Neglect friction and show that the skier will leave the hill becoming airborne at a distance of h=R/3 below the top of the hill. R is the radius of the hemispherical hill.


Homework Equations


Conservation of energy, balancing of forces, centripetal force = m(v2/r)


The Attempt at a Solution


I know this has to do with when the normal force becomes zero (or at least that's what I think). But I have no idea how to start this; can anyone point me in the right direction?
 
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