How does Newtons third law of motion explain how a real rocket travels?
This is not your usual F=ma problem because the mass of the rocket changes. It takes a little calculus, which I hope doesn’t bother you. If it does, just look at the result. The way I derive the equation is by equating the momentum of the rocket with all the fuel inside it at a given instant in time to the momentum of the rocket a short moment later plus the momentum of the fuel that has left it in the form of gases. Thus: Let u=velocity of exhaust gasses relative to rocket nozzle. This is a constant (does not depend on the rocket velocity) At some time t let : M=mass of rocket v=velocity of rocket (both of these change with time) The mometum of the rocket (which includes that of the fuel inside it) is then Mv at that instant of time t. At infinitesimal time dt later assume a mass dM of fuel has been ejected, then at the instant of time t+dt: M-dM=mass of rocket dM=mass of gases outside that was ejected during time dt v+dv=velocity of rocket v-u = velocity of ejected gases of mass dM A
