A small rocket of initial mass m 0 is fired vertically upward near the surface of the

Question:

A small rocket of initial mass m₀ is fired vertically upward near the surface of the earth (g constant). If air resistance is neglected, determine the manner in which the mass m of the rocket must vary as a function of the time t after launching in order that the rocket may have a constant vertical acceleration a, with a constant relative velocity u of the escaping gases with respect to the nozzle.