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Homework Help: Acceleration of the rocket

  1. Sep 10, 2010 #1
    1. Problem
    A launched rocket emitting gas with a speed of 1500 m/sec relative to rocket and with flowrate of 100 kg/sec.
    If net mass of rocket is 5000 kg, find it's acceleration.

    2. Equations
    Conservation of momentum
    m1u1 + m2u2 = m1v1 + m2v2

    Flowrate = 100 kg/s
    velocity = 1500 m/s
    momentum downwards = mv = 100 x 1500 = 1.5 x 105 kg m/s

    According to conservation of momentum, i found the velocity to upward direction.

    m1u1 + m2u2 = m1v1 + m2v2
    0 = -100 x 1500 + 5000v2
    5v2 = 150
    v2 = 30 m/s

    what should do next to find the acceleration
    If I use F=d(mv)/dt
    what is the initial velocity and final velocity. I have no idea about those two & and how to take it.
  2. jcsd
  3. Sep 10, 2010 #2
    usually those kind of problems are done first writing momentum at the time t, then at the time t+dt, taking difference P(t+dt)-P(t) and dividing it by dt, then you will get Newton's second law: F= dP/dt, with no external forces F = 0. If you'll get correct expression for P(t) and P(t+dt), then acceleration will pop up in dP/dt expression. just don't forget that mass is changing, and so is velocity, and that gas emitting speed is given relative to the rocket - in writing momentum you need its speed relative to inertial frame (one that is not accelerating).
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