Classical Mechanics (Kibble & Berkshire) · Problem 2.21

Newton's laws of motion and the law of gravitation — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · relative-velocity

Problem

An aircraft has cruising speed

v

and a flying range (out and back) of

R_0

in still air. Show that, in a north wind of speed

u

(

u < v

) its range in a direction whose true bearing from north is

\theta

is given by

\frac{R_0(v^2 - u^2)}{v(v^2 - u^2\sin^2\theta)^{1/2}}.

What is the maximum value of this range and in what directions is it attained?