A small rocket of initial mass m0 is fired vertically up near the surface of the earth (...

A small rocket of initial mass m₀ is fired vertically up near the surface of the earth ( g constant), and the mass rate of exhaust and the relative exhaust velocity u are constant. Determine the velocity v as a function of the time t of flight if the air resistance is neglected and if the mass of the rocket case and machinery is negligible compared with the mass of the fuel carried.