Gravitational Potential Energy of a rocket fired straight up

[genPhysics]

Homework Statement

A rocket is fired straight up from the surface of the Earth at half the escape velocity. How high will it go relative to the surface of the earth?
Neglect dissipative forces.

Homework Equations

Uinitial + Kinitial = Uf

Kf is zero

G*m*M/radius^2 + 1/2mv^2 = -G*m*M/(2R)

The Attempt at a Solution

I used the above equations and I can solve for the initial velocity. I am stuck on how to find the height. Is it just 2R?

Many thanks...physics is a struggle for me.

 

[rl.bhat]

On the surface of the earth, PE = -GMm/R and KE = 1/2*m*v^2
At a certain height, KE = 0, and PE = -GMm/(R + h)
What is the expression for the escape velocity?
From that find the initial velocity.