Speed of a Rocket far from Earth

[PhysicsMark]

Homework Statement

A rocket is launched straight up from the Earth's surface at a speed of 1.60×10^4 m/s.
What is its speed when it is very far away from the earth?

Homework Equations

F= (GMm)/r^2
G= 6.67 X 10^-11
M= 5.98 X 10^24

Potential Energy = (Gm1m2)/r
Kinetic Energy = 1/2mv^2
Escape velocity= 11200 m/s

The Attempt at a Solution

My first attempt was to take the speed of the rocket (1.60 X 10^4) and subtract it from the escape velocity. This gave me 4800 m/s. This assignment is online and the program said that answer is incorrect. Now I am not sure how to approach the problem. Does anyone have advice as to how to start this problem? All help is greatly appreciated. Thank you.

 

[D H]

Try using conservation of energy.

 

[PhysicsMark]

Conservation of energy was my second attempt. I set it up as this:

P.E. + K.E. = K.E. + P.E.


OH! I see. Dang, for some odd reason the first time I tried this approach I used 9.8 as the value for P.E. ...how foolish. I see now. Thank you so much. Man, I cannot afford to do that on a test. Thanks again.