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Homework Help: Vertically launched rocket problem with integration

  1. Oct 3, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the Rockets height as a function of time
    It is in a constant field g. u refers to the exhaust speed and M is the initial mass.
    Starts from rest. and is single stage.
    2. Relevant equations
    1) m * dv/dt= -dm/dt * u-mg

    2)Show that height as t is: y(t)= u*t- 1/2*g*t^2- u*t*ln(M/m)

    3. The attempt at a solution
    Ok, i arrived at a function very similar to the the height but, i cannot seem to get the u*t term in the function. i get y(t)= - 1/2*g*t^2- u*t*ln(M/m)
    where do i get the u*t term from? i feel like i am so close to the answer but so far away..
    I integrated 1) and arrived at V(t)= u*ln(M/m)-g*t
  2. jcsd
  3. Oct 4, 2011 #2
    no help?
  4. Oct 4, 2011 #3
    Hi, I did look at this earlier but got stuck with your first integration. It is likely there is a constant of integration you are missing so if you are still stuck and want to, please can you show me your steps to integrate 1) and then I will see if I can help?

  5. Oct 6, 2011 #4
    I'm pretty sure you're forgetting that mass is a function of time, so your integration of u*ln(M/m(t))*dt isn't as simple as you had hoped...

    Hint: Do the integration w.r.t. mass, and not time. The key here is that (I'm assuming) the fuel burn rate is constant, so dm/dt = -c, where c is some constant. Use that to replace dt with -dm/c. Also, don't forget to solve for the constant of integration using the initial condition m(0) = M.
    Last edited: Oct 6, 2011
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