A small rocket motor is used to power a "jet pack" device to lift a single astronaut above the Earth's surface. The rocket motor produces a uniform exhaust jet with constant speed, Ve = 2940 m/s. The total initial mass of the astronaut and the jet pack is Mo = 130 kg. Of this, 40 kg is fuel for the rocket motor. Develop an algebraic expression for the variable fuel mass flow rate required to keep the jet pack and astronaut hovering in a fixed position above the ground. Calculate the maximum hover time aloft before the fuel supply is expended