A small test rocket of mass 1000kg is floating freely in space, initially at rest with respect to a nearby space station. The rocket engine fires once, ejecting 50kg of exhaust gases straight backward so that the gases move away from the space station at 150m/s.
(i) Calculate the velocity of the rocket (with its remaining mass) immediately after the gases have been expelled.
(ii) Compute the increase in kinetic energy of the rocket–gas system as a result of the firing.
(iii) Explain quantitatively which part of the system (rocket or exhaust) receives the larger share of this kinetic energy and why.