solution

A rocket’s mass decreases as it burns fuel. The equation of motion for a rocket in vertical flight can be

obtained from Newton’s law, and it is

where T is the rocket’s thrust and its mass as a function of time is given by m(t) = m0(1 − rt/b). The rocket’s initial mass is m0, the burn time is b, and r is the fraction of the total mass accounted for by the fuel. Use the values T = 48,000 N, m0 = 2200 kg, r = 0.8, g = 9.81 m/s2, and b = 40 s. Determine the rocket’s velocity at burnout