Max Height of Rocket A Above Earth's Surface

[eurekameh]

A rocket of mass m=1.20x10^3 kg is launched vertically upward from the Earth's surface with an initial speed v0 = 7.00 km/s.
Calculate the maximum height H of point A above the Earth's surface at which the rocket will momentarily come to rest, before it starts falling back on the earth.

So I know energy (kinetic and potential) is conserved? I've tried using E(initial) = E(final) --> (1/2)mv0^2 = mgh, but figured this wouldn't work because g is not 9.8 m/s^2 far from the earth. Instead, I used (1/2)mv0^2 - (GMm)/Re = -(GMm)/H. I solved for H, but it did not give me the correct solution, which is 4.08 x 10^6. Can anyone help me out?

 

[Filip Larsen]

Check your use of distance in the potential energy terms.

 

[eurekameh]

Check your use of distance in the potential energy terms.

I'm supposed to use (1/2)mv0^2 - (GMm)/Re = -(GMm)/(H+Re), aren't I? Lol. Thanks!