Meriam, Kraige & Bolton — Kinetics of Systems of Particles: Problem 4_59

4/59 A small rocket of initial mass \( m_0 \) 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.