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**This is killing me!!**

A 150kg rocket moving radially outward from Earth has a speed 0f 3.7km/s when it shuts off its engine 200km above Earths surface.

(a) Assuming negligible air drag, what is the rocket's kinetic energy when it is 1000km above Earth?

(b)What is the Max height the rocket can reach?

Okay, my main issue is not solving the variables correctly. Every time I put them in my calculator I get a different answer. But maybe someone could varify my algebra and that I am using the correct values for the variables.

(a)[tex]U_i+K_i=U_f+K_f[/tex]

implies[tex]K_f=-\frac{GMm}{r_i}+\frac{GMm}{r_f}+\frac{mv^2}{2}[/tex]

Using:

[tex]r_i=6.37*10^6+2.0*10^5[/tex]

[tex]r_f=6.37*10^6+1.0*10^6[/tex]

[tex]m=150[/tex]

[tex]M=5.98*10^{24}[/tex]

[tex] v_i=3700[/tex]

then

[tex]K_f=3.8*10^7 J[/tex]

(b) I did this without relying on my answer from (a)...

[tex]-\frac{GMm}{r_i}+\frac{mv_i^2}{2}=-\frac{GMm}{r_f}[/tex]

implies[tex]\frac{2r_i}{-2GMm+r_imv^2}*(-GMm)=r_f=r_f=7.4*10^3 km[/tex]

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