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Problem with Escape Velocity given final speed

  1. Oct 18, 2012 #1
    1. The problem statement, all variables and given/known data
    The radius of Mercury (from the center to just above the atmosphere) is 2440 km (2440103 m), and its mass is 0.31024 kg. An object is launched straight up from just above the atmosphere of Mercury.
    (a) What initial speed is needed so that when the object is far from Mercury its final speed is 2500 m/s?
    vescape =


    2. Relevant equations
    1/2mvfinal^2-GMm/rfinal=1/2mvinitial^2-GMm/rfinal




    3. The attempt at a solution

    I tried to manipulate the formula algebraically. I got something like sqrt{2GM- vfinal^2}=vinitial. It's not working out. I think it has something to do with my algebra.
     
  2. jcsd
  3. Oct 18, 2012 #2
    The mass of Mercury, as given, is ridiculously small.

    The formula you have obtained is wrong dimensionally. Where is the radius of the planet in it? Perhaps you could just show the entire manipulation that gets you there.
     
  4. Oct 18, 2012 #3

    Filip Larsen

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    Gold Member

    Since the poster apparently is not aware of how to format text on this forum I assume the given mass is to be read as 0.3∙1024 kg, which fits actual data.

    I would suggest that the poster carefully checks the initial equation (which, apart from distracting formatting issues, also contains an error) and redo his calculations step by step. If the answer still mysteriously comes out wrong then by all means post the steps here for a hint or two.
     
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