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.