Solving for Horizontal Displacement: Ball on a String

[aquapod17]

Homework Statement

A ball on a string moves in a vertical circle of radius R at a constant speed with a centripetal acceleration a. At its
lowest point, the ball is a negligible height above the ground. After several revolutions, the string breaks at the highest
point in the motion. In terms of R, a, and g, find the horizontal displacement of the ball from the time the string breaks.

Homework Equations

a_c=v²/r

The Attempt at a Solution

I found v = √a_cr but I don't know where to go from here.

 

[LowlyPion]

If it breaks at it's highest point, what direction will the ball be traveling?

How high off the ground was it when it was released?

Doesn't it just become a simple kinematic problem?

 

[aquapod17]

If it breaks at its highest point it will travel horizontally first, but then reach the ground.

It is 2R off the ground when it was released.

OMG I GOT IT! Thanks so much! I just had trouble manipulating the equation. Embarrassing.