Classical Mechanics (Kibble & Berkshire) · Problem 10.7

The angular momentum principle — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · rocket-motion

Problem

A rocket of initial mass

M

, of which

M-m

is fuel, burns its fuel at a constant rate in time

\tau

and ejects the exhaust gases with constant speed

u

. The rocket starts from rest and moves vertically under uniform gravity. Show that the maximum speed achieved by the rocket is

u\ln\gamma

and that its height at burnout is

u\tau\left(1 - \frac{\ln\gamma}{\gamma-1}\right),

where

\gamma = M/m

. [Assume that the thrust is such that the rocket takes off immediately.]