A 50-kg model rocket lifts off by expelling fuel downward at a rate of k = 4.75 kg/s for
Chapter 9, Problem 63(choose chapter or problem)
A 50-kg model rocket lifts off by expelling fuel downward at a rate of k = 4.75 kg/s for 10 s. The fuel leaves the end of the rocket with an exhaust velocity of b = 100 m/s. Let m(t) be the mass of the rocket at time t. From the law of conservation of momentum, we find the following differential equation for the rockets velocity v(t) (in meters per second): m(t)v (t) = 9.8m(t) + b dm dt (a) Show that m(t) = 50 4.75t kg. (b) Solve for v(t) and compute the rockets velocity at rocket burnout (after 10 s).
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