Please only answer the (c) part of the question.

A windmill has three identical blades of length I, mass m and negligible width, equally separated by 120, rotating around a pivot point, located at height I + h above the ground. Initially the windmill is not moving and there are no external forces. The lowest blade is vertical, so its lowest point will be at height h above ground. All frictions can be neglected. (a) Derive the moment of inertia of the windmill about the pivot. (b) A person stands at the side of the windmill, at a distance d from its base, along the direction defined by the plane containing the blades. He throws a stone with mass ms with initial velocity 7 at an angle a with respect to the horizontal plane. Derive an expression for the distance d such that the stone hits the bottom of the lowest blade when the stone is at its maximal height (i.e. the vertical component of the stone's velocity is zero). Also derive an expression for h as a function of a and v. h (c) The stone hits the blade and sticks to it, putting the windmill in motion. Derive an expression for the initial angular velocity of the windmill after the collision (also considering the moment of inertia of the stone)