Escape velocity

Here is the problem.

A rocket of mass m is in a circular orbit around the Earth at a distance R from the center.
(a) What tangential impulse, mΔv, must be given to the body so that it just escapes to infinity?

My attempt:
I set the problem in terms of energy, E=1/2m((dr/dt)^2+r^2(dø/dt)^2) V(r) and using conservation of angular momentum I get

dr/dt=[2mMG/r-(l/mr)^2]^1/2,
where l=mr^2dø/dt.

Am I missing something?

Thank you.

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