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Rocket ascending in Earth's gravity

  1. Jun 21, 2011 #1
    1. The problem statement, all variables and given/known data
    A rocket ascends from rest in Earth's gravitational field, by ejecting exhaust with constant speed u. Assume that the rate at which mass is expelled is given by dm/dt = −γm where m is the instantaneous mass of the rocket and γ is a constant; and that the rocket is retarded by air resistance with a force mbv where b is a constant.
    Determine the velocity of the rocket as a function of time. Here is a hint: The terminal velocity is ( γu−g )/b.

    Calculate the time when the velocity is one-half of the terminal velocity.
    Data: u = 31.9 m/s; b = 1.2 s−1.


    2. Relevant equations
    dp/dt=F=m(dv/dt)



    3. The attempt at a solution
    I get dv=-udm-(g+bv)dt; dm=-γm
    so dv=uγ-(g+bv)dt

    solving for v:
    v(t)=(1/b)e^((-uγ/b)t)-(g/b)

    the problem I am running into is what is gamma, because I have no inital condition to apply, and I'm fairly sure the solution to the diff eq is correct.
     
  2. jcsd
  3. Jun 22, 2011 #2
    gamma is just a constant, it doesn't really matter what it is, your answers will probably just have to be expressed in terms of it.
     
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