Question

A rocket ascends from rest in a uniform gravitational field by ejecting exhaust with constant speed u. Assume that the rate at which mass is expelled is given by dm/dt = m where m is the instantaneous mass of the rocket and is a positive constant, and the rocket is retarded by air-resistance with a force mv, where b is a constant. Find the velocity of the rocket as a function of time

Answer 1

Answer:

rocket ascends from rest in a uniform gravitational field by ejecting exhaust with constant speed u. Assume that the rate at which mass is expelled is given by dm/dt=ms, where m is is the instantaneous mass of the rocket and s is a cosntant, and that the rocket is retarded by air resistance with a force bv where b is a constant. find the velocity of the rocket as a function of time. in my text they have proven the case when the total external force is F and it equals: F=mdv/dt+udm/dt, i used this in the calculation, and got: mg-bv=mdv/dt+udm/dt, but i dont think this correct, your help as always is appreciated. Newtons third law applies, you know, the equal but oppisite force one. The force that the mass leaving excerts on the rocket the rocket exerts on the mass. Then we are left with: mass. Then we are left with: m ∗ d v d t = − v d m d t

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