Gravitational Potential and Kinetic Energy

[yttuncel]

Homework Statement

A rocket is propelled vertically upward from the Earth which has a radius R₀. After
its fuel has become exhausted, the rocket reaches its highest point at a height of 2R₀
above the surface of the Earth and then falls vertically down back to the earth. With
what speed does the rocket strike the surface of the earth? Air resistance is negligible.
Express in terms of R₀ and g at the surface of the earth. Show clearly your reasoning.

Homework Equations

U=-GMm/R KE=1/2mV²

The Attempt at a Solution

So I did everything accordingly, I ΔU + ΔK = ΔE which is 0. So -ΔU = ΔK. But my answer includes mass which the question does not want, what am i doing wrong? Shall I use another formula-relation ?

 

[Doc Al]

So I did everything accordingly, I ΔU + ΔK = ΔE which is 0. So -ΔU = ΔK. But my answer includes mass which the question does not want, what am i doing wrong? Shall I use another formula-relation ?

I assume your answer includes the mass of the earth? If so, you can get rid of it by expressing things in terms of g and R₀. (What's an expression for g?)

 

[yttuncel]

g=Gm/r^2 . Ok thanks! I confused g with G.