1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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?

    Cheers
     
  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...

    Edit:
    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Vertically launched rocket problem with integration
  1. Rocket Launching (Replies: 1)

Loading...