Consider a small single-stage rocket launched vertically. Let m(t) denote the total mass...

Consider a small single-stage rocket launched vertically. Let m(t) denote the total mass of the rocket at time t (which is the sum of three masses: the constant mass of the payload, the constant mass of the vehicle, and the variable amount of fuel). If it is assumed that the positive direction is upward, air resistance is proportional to the instantaneous velocity ν of the rocket, and R is the upward thrust or force generated by the propulsion system, then find a mathematical model for the velocity ν(t) of the rocket. [Hint: See (14) in Section 1.3 and (18) in Exercises 1.3.]