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Homework Help: Rocket momentum question.

  1. Feb 21, 2010 #1
    1. The problem statement, all variables and given/known data
    A rocket that starts at rest with mass M ejects exhaust at a given speed u. what is the mass of the rocket(including unused fuel) when its momentum is maximum?

    2. Relevant equations


    3. The attempt at a solution
    well basically i used conservation of momentum to get the velocity of the rocket with respect to mass. after doing all the integrating work i got v=uln(M/m) assuming that m is the mass of the rocket at a later time. plugging the velocity into the p=mv formula i differentiate with respect to mass where the equation becomes dp/dm=u[ln(M/m)-1/m^2]. now i set dp/dm to zero to try to find the mass needed for a max momentum but unfortunately the dp/dm equation isn't easy to solve due to the "ln" function. Am i doing something wrong here?
  2. jcsd
  3. Feb 22, 2010 #2


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    Science Advisor
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    Gold Member

    I don't believe you took the derivative correctly because dp/dm must have dimensions of speed. Your expression does not. Remember the chain rule.
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