A "kinetic kill" missile destroys its target through conversion of kinetic energy to mechanical work. That is, there is no explosion-it destroys the target only by means of the collision. Consider a missile with a rocket engine flying a straight-line path to a target. Suppose the engine has a mass flow rate of 0.5 kg/sec and an exhaust velocity of 1 km/s relative to the rocket. Assuming that the missile body has a mass of 1,000 kg, find the total mass of fuel necessary to achieve a final kinetic energy of 5 × 106 J.