Special relativity

(a) A rocket propels itself along a straight line in empty space by burning its fuel in such a way that the velocity of the exhaust gases ejected from the nozzle is v0 in the instantaneous (inertial) rest frame of the rocket. If the rocket starts from rest with a total mass Mi (icluding fuel), find the relationship between its velocity and mass during its journey. (b) Typical chemical fuels yield exhaust speeds of the order of 103 m/s. Let us imagine we had a fuel that gives v0 = 3 × 105 m/s. What initial mass of fuel would the rocket need in order to attain a final velocity of 0.1c for a final mass of 1 ton? (c) Matter-antimatter fuel yields v0 = c = 1 (the exhaust consists of photons). What initial mass of fuel would be required in this case (in order to attain a final velocity of 0.1c for a final mass of 1 ton)?