# When will the ball fly?

A ball, modelled as a particle, sits on a smooth semicircle with a height $$h$$ from the ground. There is a gravitational pull, $$g$$, on the ball acting straight down. The ball slides down the side of the semicircle. The height at which the ball will slide of is $$k$$. We have the relationship $k=\frac{a}{b}h$ Where $$a$$ and $$b$$ are positive coprime integers. Find $$a+b$$.

Details and Assumptions

• Take $$g=9.8\ \mathrm{m}\ \mathrm{s}^{-2}$$

• $$h$$ is strictly less than the radius of the semicircle.

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