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Accelerating rocket w/ changing mass *need to finish tonight!*

  1. Nov 22, 2009 #1
    1. The problem statement, all variables and given/known data
    Prove that the upward velocity of a rocket of initial mass M0, which is propelled by fuel burning at a rate of R kg/s, is given by vy = uex * ln[M0 / M(t) ] - g * t. uex is the speed of the exhaust gas relative to the rocket and M0 is the initial mass (rocket + fuel).

    Also find the initial velocity and acceleration and velocity at time = 180s.

    M0 = 2.12E6 kg
    Fth = 2.32E7 N (Force of thrust)
    R = 4.6E3

    M(t) = M0 - R * t
    Fth = -R * uex

    2. Relevant equations

    ?


    3. The attempt at a solution
    Well it seems like I can get all the required values I need, but I still need to prove the given formula, and I'm not really sure where to start and I'm hoping for some tips.


    EDIT: Would finding the rate of changing for the rocket's acceleration be a start? (ie x m*s^3)
     
    Last edited: Nov 22, 2009
  2. jcsd
  3. Nov 22, 2009 #2
    No one can provide any help? I desperately need some.
     
  4. Nov 22, 2009 #3

    D H

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    Finding the rocket's acceleration would be a good start.
     
  5. Nov 22, 2009 #4
    So applying newton's second law I ended up with:

    (Fth / m) - g = a

    But m is dependent on time so that becomes:

    [Fth / (m0 - R * t)] - g = a

    Do I then have to integrate that somehow?
     
  6. Nov 22, 2009 #5
    Anyone?
     
  7. Nov 22, 2009 #6

    D H

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    How hard is that to integrate?
     
  8. Nov 23, 2009 #7
    It's been a while since I've taken calculus, I'm not really sure how to.
     
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