When the person at the top of the spherical surface the weight of the person is equal to the normal force on the
person .And at the top of the spherical surface it has only the potential energy
when the person at point of leaves the surface there is kinetic energy and the potential energy .
At the top of the surface
N = mg
At an angle θ
mg cosθ - N = mV2/r
But at angle θ normal force is zero
mg cosθ = mV2/r
V2= r g cosθ -----------(1)
From the conservation of enrgy at top and at an angle θ is
mgr = mgh + (1/2)mV2
2gr = 2gh + V2
V
2 =
2gr - 2gh
= 2gr - 2g( rcosθ) ----------(2)
From the equations we get the value of the angle θ = ---------- degrees