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Homework Help: Speed of a Rocket far from Earth

  1. Nov 26, 2009 #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 1.60×10^4 m/s.
    What is its speed when it is very far away from the earth?

    2. Relevant equations
    F= (GMm)/r^2
    G= 6.67 X 10^-11
    M= 5.98 X 10^24

    Potential Energy = (Gm1m2)/r
    Kinetic Energy = 1/2mv^2
    Escape velocity= 11200 m/s

    3. The attempt at a solution

    My first attempt was to take the speed of the rocket (1.60 X 10^4) and subtract it from the escape velocity. This gave me 4800 m/s. This assignment is online and the program said that answer is incorrect. Now I am not sure how to approach the problem. Does anyone have advice as to how to start this problem? All help is greatly appreciated. Thank you.
  2. jcsd
  3. Nov 26, 2009 #2

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    Try using conservation of energy.
  4. Nov 26, 2009 #3
    Conservation of energy was my second attempt. I set it up as this:

    P.E. + K.E. = K.E. + P.E.

    OH!!!!!!!!!!!! I see. Dang, for some odd reason the first time I tried this approach I used 9.8 as the value for P.E. ...how foolish. I see now. Thank you so much. Man, I cannot afford to do that on a test. Thanks again.
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