A rocketĂ˘â‚¬â„˘s mass decreases as it burns fuel. The equation of motion for a rocket in vertical flight can be
obtained from NewtonĂ˘â‚¬â„˘s law, and it is
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where T is the rocketĂ˘â‚¬â„˘s thrust and its mass as a function of time is given by m(t) = m0(1 Ă˘Ë†â€™ rt/b). The rocketĂ˘â‚¬â„˘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 rocketĂ˘â‚¬â„˘s velocity at burnout