A solid sphere and a hoop have the same radius R and the same mass M. They are each released from rest from the same height H at the top of an…

A solid sphere and a hoop have the same radius R and the same mass M. They are each
released from rest from the same height H at the top of an inclined plane. They roll
without slipping to a point of height h then leave the ramp at an angle (Theta). They reach a
maximum height Y above the ground and land a horizontal distance D from the launch
point.
a) Derive an expression for the angular speed of an object at the apex of flight. Simplify as
much as possible. Hint: Are there external torques on a projectile?
b) Derive an expression for the distance D. Simplify as much as possible. Which object
travels further? Explain this in terms of energy conservation.
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