Calculating Rocket Speed at a Distant Location

[bcjochim07]

Homework Statement

A rocket is launched straight up from the Earth's surface at a speed of 15,000 m/s. What is its speed when it is very far away from earth?

Homework Equations

K=.5mv^2
U=-GMm/R

The Attempt at a Solution

Is this correct: I used conservation of energy and assumed very far was where U=0

(.5)(m)(15000m/s)^2 + -[(6.67*10^-11)(5.98*10^24)m]/[6.37*10^6m)=.5mv^2
v=9988 m/s

Also could someone explain to me why potential energy decreases with increasing height in this case as opposed to increasing U by lifting an object above the ground on earth.

Thanks

 

[alphysicist]

Your equation looks okay to me.

Also could someone explain to me why potential energy decreases with increasing height in this case as opposed to increasing U by lifting an object above the ground on earth.

It doesn't; the potential energy is a negative number that get closer to zero with increasing height (i.e., distance away from the earth), which means it is increasing.

 

[bcjochim07]

Oh yeah. I see exactly what you are saying. Thanks!