IB Physics Rate of Change of Momentum

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A tutorial sheet on the rate of change of momentum follows. What does it mean?

  1. A rocket moves through space. At a certain instant its mass is m and its speed relative to the Earth is u. At this instant it is ejecting mass backwards at a rate m' at a speed v relative to the Earth. What is the resultant force acting on the rocket at this instant? Assume u and v are much less than c.
  2. In question 1 the rocket is ejecting mass backwards at a speed w relative to the rocket. Find the force acting on the rocket at this instant. Assume u and w are much less than c.
  3. In which question, 1 or 2, does the rocket have greater speed after a given time if w = v?
  4. In question 1 is the acceleration of the rocket relative to the Earth constant?
  5. Find the total momentum of the fuel-rocket system at time t.
  6. In question 1 the rocket is initially at rest. If m = 25.0 kg, v = 100.0 m s-1 and m' = -0.5 kg s -1, show that at t = 10.0 s, u = 25.0 m s-1 and s = 115.7 m, where s is the distance travelled by the rocket as it burns fuel.
  7. In question 2 the rocket is initially at rest. If m = 25.0 kg, w = 100.0 m s-1 and m' = -0.5 kg s -1, show that at t = 10.0 s, u = 28.125 m s-1 and s = 125 m.