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!

Rocket problem: Newton's 2nd Law

  1. Feb 22, 2010 #1
    1. The problem statement, all variables and given/known data
    In this problem we explore a slightly more realistic model of a rocket's acceleration still neglecting air resistance. Consider a rocket fired straight up from rest burning fuel at the constant rate of b kg/s. Let v=v(t) be the velocity of the rocket at time t and suppose that the velocity u of the exhaust gas is constant. Let m=m(t) be the mass of the rocket at time t, and note that m is not constant. From Newton's second law it can be shown that F=m(dv/dt) - uv where the force F= -mg and g is acceleration due to gravity, thus, m(dv/dt) - uv = -mg. Let M1 be the mass of the rocket without fuel and M2 be the initial mass of the fuel.

    a. Find an equation for the mass m at time t in terms of M1, M2, and b.
    b. Substitute this expression for m in equation one and solve the resulting equation for b. Use separation of variables.
    c. Determine the velocity of the rocket at the time that the fuel is exhausted. This is called the burnout velocity.
    d. Find the height of the rocket at the burnout time.


    2. Relevant equations
    See Newton's 2nd Law above.


    3. The attempt at a solution
    I honestly don't even know how to start this problem, so any help would be greatly appreciated. Thank you!
     
  2. jcsd
  3. Feb 23, 2010 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi hana! :smile:
    ok, start with a. …

    what is the mass m at time t in terms of M1, M2, and b ?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook