Suppose that a rocket is launched vertically and it is known that the exaust gases are emitted at a constant velocity of 18.5 m/s relative to the rocket,

Question

Suppose that a rocket is launched vertically and it is known that the exhaust gases are emitted at a constant velocity of 18.5 m/s relative to the rocket, the initial mass is 1.4 kg and we take the acceleration due to gravity to be 9.81 ms^−2

(a) If it is initially at rest, and after 0.6 seconds the vertical velocity is 3.79 m/s, then what is α, the rate at which it burns fuel, in kg/s?

Enter your answer to 2 decimal places.

(b) How long does it take until the fuel is all used up? Enter in seconds correct to 2 decimal places.

(c) If we assume that the mass of the shell is negligible, then what height would we expect the rocket to attain when all of the fuel is used up? Enter an answer in meters to decimal places.

(Hint: the solution of the DE doesn't apply when m(t)=0 but you can look at what happens as m(t)→0 The limit lim x -> 0^+ x ln x = 0 may be useful).



Enter in meters (to the nearest meter)

Answer 1

Use momentum conservation law. Remember that p = m v, and dp/dt = 0. Since mass is changing this implies v dm/dt + m dv/dt = 0 for the rocket + fuel system.