Gravitational Potential Energy of a rocket

[mcnealymt]

Homework Statement

A rocket is launched straight up from the Earth's surface at a speed of 1.80×104m/s . What is its speed when it is very far away from the earth? Answer in m/s

Homework Equations

K1+U1=K2+U2

The Attempt at a Solution

.5mV1^2-(G*m*Me)/r= .5mV2^2-(G*m*Me)/r
*** THe mass of the rocket should cancel out and the U1 aka (g*m*Me)/r should be zero.

you are left with:

.5V1^2=.5V2^2-(G*m*Me)/r
*** Now solve for V1

V1 = Square root of [ (.5V1^2+(GMe)/r)/.5 ]

I got 1.06 *10^4

what am I doing wrong? I know that you have to use conservation of energy and assume that since the rocket is traveling a very far distance the final potential energy is going to be zero. Could it be calculator issues?!

 

[TSny]

.5V1^2=.5V2^2-(G*m*Me)/r
*** Now solve for V1

V1 = Square root of [ (.5V1^2+(GMe)/r)/.5 ]

Watch the signs, and I think you meant V2 instead of V1 in the square root. I'm assuming that you are letting "1" stand for final and "2" for initial.

 

[rude man]

Why did you say U1 = 0? It's not.
Then: what is U2?

 

[Chestermiller]

Your original equation is correct, but your implementation of it is incorrect. The r that goes along with V1 is the radius of the earth, and the r that goes along with V2 is infinite. Also, you need to check over your algebra...you have a problem with those 0.5's.