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Gravitational Potential Energy of a rocket

  1. May 3, 2013 #1
    1. The problem statement, all variables and given/known data
    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



    2. Relevant equations
    K1+U1=K2+U2



    3. 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?!?!?!
     
  2. jcsd
  3. May 3, 2013 #2

    TSny

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    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.
     
  4. May 3, 2013 #3

    rude man

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    Why did you say U1 = 0? It's not.
    Then: what is U2?
     
  5. May 3, 2013 #4
    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.
     
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