Meriam, Kraige & Bolton — Kinetics of Systems of Particles: Problem 4_81

4/81 A small rocket of initial mass \( m_0 \) is fired vertically up near the surface of the earth (\( g \) constant), and the mass rate of exhaust \( m' \) 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.