Centripetal/Projectile Motion: Proof of Formulas for v^2=mgy

[oridniv]

from the second question in the link, I've been asked to figure out how to proof some of the formulas. Could someone please help me? I tried using some formulas but I keep getting stuck. If it doesn't show, then could someone please help me proof the formula v^2=mgy

file:///C:/Documents%20and%20Settings/Jenny/Desktop/physics%20assignment2.htm

 

[a9211l]

none of us can access a file on your computer, you're going to have to post the question manually.

 

[oridniv]

A ball on a string is released from rest with the string horizontal and swings through a quarter circle of radius R. At the bottom of the swing the string breaks and the ball is launched horizontally with speed v. The bottom of the swing is a distance 2R above the floor and the ball lands on the floor a distance d away. I'm using v for velocity, R for radius, and g gravity and a for accelaration
We have to prove that v^2=2gR

I used the formula v^2y-v^2oy=2ay(y-yo)
My final answer was -v^2=4gR...something's wrong here because i need help

 

[NeoDevin]

First: This should be posted in Homework Help.

Second: You can use conservation of energy here to solve it.