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Help with final velocity of a rocket

  1. Oct 24, 2012 #1
    1. The problem statement, all variables and given/known data
    Calculate the final velocity of a rocket if the velocity of the ejected gas is c, initial mass of rocket is M0 and final mass is Mr, v0=0.


    2. Relevant equations
    We have to calculate the final velocity of rocket.


    3. The attempt at a solution
    Because the total momentum of an isolated system is conserved, the total system - rocket + exhausted gas - must still have zero momentum.
    If the velocity of gas is c, then:
    M0*v - (M0-m)*c=0
    m - mass of gas ejected

    What to do next?
     
  2. jcsd
  3. Oct 24, 2012 #2

    tiny-tim

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    Welcome to PF!

    Hi PhysicsLoop! Welcome to PF! :smile:
    Ah, but you don't know what the final velocity of the gas is (it changes according to the velocity of the rocket at the time).

    You'll need to write a differential equation for what happens when the speed is v and the mass is m, and a small amount of mass dm is ejected. :wink:
     
  4. Oct 24, 2012 #3
    Thanks! :)
    Velocity of the gas is constant equal with c (speed light), it doesn't change with rocket velocity.
    Can you help me? I'm stucked.
     
  5. Oct 24, 2012 #4

    tiny-tim

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    v is a function of m

    write the equation for conservation of momentum when the mass changes from m to m - dm
     
  6. Oct 24, 2012 #5
    I still don't get it... Can you write it please?
     
  7. Oct 25, 2012 #6
    Can someone help me with this?
     
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