Calculating Angle θ in Rotating Ball at Point P - Energy + Other Stuff

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Homework Statement



As shown below, a ball is tied to one end of a string and the other end is fixed at point P. The ball is rotating about a vertical and at the top of its path has a speed v= (gr)^0.5 (don't know how to make a square root sign). At what angle θ should the sting be cut so that is passes through the center of the circle

https://mail.google.com/mail/?ui=2&ik=3fce58663c&view=att&th=12bebfdb82278d47&attid=0.1&disp=inline&zw


This is my first post, if i haven't correctly followed protocol please inform me. thanks in advanced for all the help.
 

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oh yea the speed of the ball is not constant. ie faster at the botton than the top.
 
You need to show some attempt to solve the problem.

This is a circular motion in a vertical plane at start. You know the speed at the top. Use conservation of energy to find the speed at an arbitrary angle.

After the string has been cut, the ball is a projectile. Express the vertical and horizontal components of the initial velocity in terms of the angle. Use the equation between the horizontal and vertical coordinates of the projectile so as it goes through the centre.

So collect the relevant formulas. Try to use them.

ehild