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Help with gravitation proof

  1. May 3, 2009 #1


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    1. The problem statement, all variables and given/known data
    A rocket accelerates to speed v0 near the earth's surface,and then coasts upwards. Show that if
    v0 = 2sqrt(gR)
    where R is the Earth's radius, then very far from the earth the rockets speed will be
    v = sqrt(2gR)

    2. Relevant equations
    The only equations I have thought of that may help are:
    Escape Velocity:
    v = sqrt(2GM/R)
    Gravitational potential energy:
    U= -GMm/r

    3. The attempt at a solution
    I have attempted using energy conservation and solving for v, however the answer appears far from that required.
    This lead me to think that perhaps linear approximation may be required but I am unsure how I would apply (1+x)n = 1+nx for x<<1 in this problem.
  2. jcsd
  3. May 3, 2009 #2


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    Welcome to PF!

    Hi K29! Welcome to PF! :smile:

    (have a square-root: √ :wink:)
    Yes, those equations should do it …

    but they use G, not g …

    so what is the formula connecting G and g (and R)? :smile:
  4. May 4, 2009 #3


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    Ah yes. Thank you. All I needed to do was manipulate the final answer that I had from enegry conservations a tiny bit and then substitute that formula in

    uhm as a new user,... am I meant to reply once I've got an answer??
    I like the style of answering questions. Better than just copying an answer. "Help" is the way to go. At least that way I know where I've gone wrong
  5. May 4, 2009 #4


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    Hi K29!

    Yes, it's friendlier if people reply. :smile:

    Otherwise we tend to assume that they got a complete answer to the same question on another site, and never bothered with the hints from this site. :rolleyes:

    The hints, btw, are the characteristic policy of PF … Greg Bernhardt :smile: reckons that members learn better if they have to do most of the work themselves!

    See you around! :wink:
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