Two missiles A and B powered by solid rocket motors have identical specific impulse, liftoff mass of 5600 kg each, and burn durations of t_A = 30 s and t_B = 70 s respectively. The propellant mass flow rates, ṁ_A and ṁ_B for missiles A and B, respectively, are given by ṁ_A = 120 kg/s, 0 ≤ t ≤ 30 and ṁ_B = 70 kg/s, 0 ≤ t ≤ 70. Neglecting gravity and aerodynamic forces, the relationship between the final velocities V_A and V_B of missiles A and B, respectively, is given by