Rocket Motion Suppose a small single-stage rocket of total mass m(t) is launched

Chapter 2, Problem 44

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Rocket Motion Suppose a small single-stage rocket of total mass m(t) is launched vertically and that the rocket consumes its fuel at a constant rate. If the positive direction is upward and if we take air resistance to be linear, then a differential equation for its velocity v(t) is given by dv k-A R -+ v = -g + dt m0 - At m0 - At' where k is the drag coefficient, A is the rate at which fuel is consumed, R is the thrust of the rocket, m0 is the total mass of the rocket at t = 0, and g is the acceleration due to gravity. See in Exercises 1.3. (a) Find the velocity v(t) of the rocket if m0 = 200 kg, R = 2000 N, A = 1 kg/s, g = 9.8 m/s 2 , k = 3 kg/s, and v(O) = 0. (b) Use dsldt = v and the result in part (a) to find the height s(t) of the rocket at time t.