Particle on top of a half circle

[gralla55]

Homework Statement

A point-particle sits at rest at the top of a half-circle with radius R. Find the minimum initial velocity v0 the particle has to have in order to clear the half circle without rolling down on one of its sides.

Homework Equations

None are given.

The Attempt at a Solution

Since the radius is given as a variable, I'm guessing it should be possible to write the solution as a function of R and g. The only thing I've managed to write down is:

v0x = ?
v0y = 0
ax=0
ay=g

Any help on how to proceed? I have no idea how to make sure the particle clears the circle... I thought about solving for the initial velocity needed to make sure the particle travels farther than R before hitting the ground, but the path will be a parabola and not a circular path, so again I'm not sure. Thanks!

 

[grzz]

... I thought about solving for the initial velocity needed to make sure the particle travels farther than R before hitting the ground...

I think you are on the right track.