Pendulum/Circular Motion Problem

1. The problem statement, all variables and given/known data

A small ball of mass m is attached to a very light string of length L that is tied to a peg at
point P. What is the magnitude of the horizontal velocity that must be applied to the ball
so that it swings up and lands on the peg? Your answer can only contain the given
information and any appropriate physical constants (such as g).
If you have the acceleration of gravity g in your answer do not
substitute numbers for it. You may introduce other variables to
help you reach a solution but your final solution can only
contain the given variables and g.
(SEE ATTACHED)
2. Relevant equations

Conversation of Mechanical Energy?

3. The attempt at a solution

My initial thought was to set ΔK=ΔP since gravity is a conservative force and the only displacement is vertically, the length of the string. That gave me an initial velocity of √2gL

Attached Images
File Type: png Screen Shot 2014-04-12 at 12.36.03 PM.png (27.5 KB)

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