Classical Mechanics (Kibble & Berkshire) · Problem 10.9
The angular momentum principle — T.W.B. Kibble, F.H. Berkshire
Physics — Mechanics · rocket-motion
Problem
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 −ϵkv, where v is the forward velocity of the rocket, and ϵ 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 ϵ is small.