I don\'t understand the second part of the question. A child is sledding on a se

Question

I don't understand the second part of the question.

A child is sledding on a semi-circular hill as shown, starting from rest at the top of the hill. Assume a frictionless surface At some point down the hill the sled leaves the surface. Draw a free-body diagram for the sled at an arbitrary angle theta When the sled leaves the surface, the normal force is zero. Calculate where this happens (ie, at what value of the angle theta). (Hint: at that instant consider the motion to be uniform circular motion).

Explanation / Answer

by energy conservation,
mgr ( 1-sin) = 1/2 mv2

and from centripetal acceleration , with normal force zero,

mv2 / r = mg sin

From 2 equations,

2- 2 sin = sin

=> sin = 2/3

=> = 41.810

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