Law of conservation of linear momentum for a system of particles is the underlying principle

that governs the operation of a rocket. In this regard, in rocket propulsion, the system is the rocket and its ejected fuel (gases). As a rocket moves, because the gases are ejected with certain linear momentum, the rocket receives an equal magnitude of momentum in the opposite direction. Thus the rocket accelerates as a result of 'thrust' from the exhaust gases. If the gases are ejected with a speed V e relative to the rocket, it can be proved that M dV = V e dm where dV is a small increase in the speed of the rocket as a result of burning of fuel of mass dm. M is the mass of rocket and its remaining fuel after an amount of fuel having a mass dm has been ejected. Integration of this equation with suitable limits will result in a basic expression for rocket propulsion.

Consider a rocket having an initial mass 1000 kg which also includes the mass of fuel. The rocket is fired and it burns fuel at a constant rate 25 kg/s. the speed of exhaust gases relative to the rocket is a constant 2000 m/s.

Answer these questions:

(i) Thrust provided by the rocket engine is –