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+[/COLOR](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.

 

[Nickie]

Your approach and equations are correct, but the final answer you got may be due to rounding errors in your calculator. The correct answer is 1.06*10^4 m/s. It is important to use the full values of all the variables and not round off until the final step to avoid any errors. Also, make sure you are using the correct values for the gravitational constant (G) and the mass of the Earth (Me).