Rocket in resisting medium A rocket of initial mass M, of which M - m is fuel, burns its fuel at a constant rate k and ejects the exhaust gases with constant speed u. The rocket starts from rest and moves through a medium that exerts the resistance force -?kv, where v is the forward velocity of the rocket, and ? is a small positive constant. Gravity is absent. Find the maximum speed V achieved by the rocket. Deduce a two term approximation for V, valid when ? is small.