How Fast Are Rockets Moving at Moon's Orbit?

[darklich21]

Homework Statement

Two rockets are launched from Earth's surface, one at 17 km/s and the other at 22 km/s. How fast is each moving when it crosses the moon's orbit?

Homework Equations

Kf + Uf= K0 + U0
0.5mvf^2 -GMm/R = 0.5mv0^2 - GMm/R

The Attempt at a Solution

So I attempted to use the equation above, using the Earth's mass and the Earth's radius, It didn't work, my speeds came out to be exactly 17 and 22 just like from the start. I'm going to say that the radius of the moon and the mass of the moon comes into play here. Can someone help, with perhaps a better equation?

 

[superdave]

Radius in this case the distance from M, and is different on each side of the equation. So it's R_1 and R_2. You could use the center of the Earth or the surface of the Earth as the origin, as long as you are consistent. the surface is probably easier. So the radius at the start is 0. And the radius at the moon is the distance from the Earth to the moon. Ignore the actual moon. it's not important here.

You should be able to handle it from here.

 

[darklich21]

how can the radius be 0, the radius in my equation is in the denominator. it would make 1 part of the expression undefined

 

[darklich21]

nvm i figured it out, but I am going to correct your response. The radius is NOT 0, but instead the raidus of the earth, while on the other side of the equation, it's the radius of the Earth + the distance to the moon.