You are designing a single-stage rocket to launch a 300-kg satellite. Assume the rocket engine's I, as 460 sec. Use g = 9.8 m/sec for the gravity acceleration constant. (a) Assume that you are launching the satellite in free space with no gravity and no aerodynamic drag, and your rocket has zero mass except the propellants and the satellite. Calculate the mass of the propellants to give AV = 7.784 km/sec. [10 pts] (b) Assume the same in (a) except that the rocket's mass is proportional to the propellants: 15% of the propellants. Calculate the mass of the propellants for AV = 7.784 km/sec. (Of course, the rocket's mass remains the same after the burn) [15 pts]