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A skier plans to ski a smooth fixed hemisphere of radius r. He starts from rest from a curved smooth surface of height (R/4). The angle theta at which he leaves the hemisphere is

A skier plans to ski a smooth fixed hemisphere of radius r. He starts from rest from a curved smooth surface of height (R/4). The angle theta at which he leaves the hemisphere is 

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Grade:12th pass

1 Answers

Arun
25763 Points
2 years ago
∆h=R/4+R(1–cosθ)
½ mv^2 =mg∆h= mgR/4 {1+4(1–cosθ)}
mv^2/R =  mg (5 − 4 cos θ) /2

mgcosθ–N= mv^2/ R
mgcosθ= mg(5−4cosθ)/ 2
cosθ = 5/6

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