Multi-stage rocket in empty space a rocket in zero gravitational field has a mass of mri = 2.81 x 107 kg, which is the sum of the mass of the fuel mi = 2.46 x 107 kg and the dry mass of the rocket (empty of fuel) mr. d = mri - mi = 0.35 x 107 kg. the fuel is ejected at a speed u = 3000 m/s relative to the rocket. the total burn time is 510 s and the fuel is burned at a constant rate. (a) what is the final speed us of the rocket in meters/second after all the fuel is burned assuming it starts from rest? (b) now suppose that the same rocket burns the fuel in two stages, expelling the fuel in each stage at the same relative speed u = 3000 m/s. in stage one, the available fuel to burn is m f. l.4 = 2.03 x 107 kg with burn time 150 s. the total mass of the rocket after all the fuel in stage 1 is burned is mr. l.d = mri - m/.1.= 0.78 x 10' kg. what is the change in speed after stage one is complete? (c) next, the empty fuel tank and accessories from stage one are disconnected from the rest of the rocket. these disconnected parts had a mass m = 1.4 x 100kg, hence the remaining dry mass of the rocket is m, 2.d = 2.1 x 100 kg. all the remaining fuel with mass m2i = 4.3 x 106 kg is burned during stage 2 with burn time of 360 s. what is the change in speed in meters/second after stage two is complete? (d) what is the final speed in meters/ second of the rocket after both stages are complete? (e) how does this compare to your answer to part a for the final speed if all the fuel were burned in one stage? does your answer make sense?