In 21, the mass m(t) is the sum of three different masses:

Chapter 1, Problem 1.1.133

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In 21, the mass m(t) is the sum of three different masses: where mp is the constant mass of the payload, mv is the constant mass of the vehicle, and mf(t) is the variable amount of fuel. (a) Show that the rate at which the total mass m(t) of the rocket changes is the same as the rate at which the mass mf(t) of the fuel changes. (b) If the rocket consumes its fuel at a constant rate , find m(t). Then rewrite the differential equation in in terms of and the initial total mass m(0) m0. (c) Under the assumption in part (b), show that the burnout time tb 0 of the rocket, or the time at which all the fuel is consumed, is where mf(0) is the initial mass of the fuel