Question

An airplane flies at a speed of 250 mi/hr, 40 degrees south of east. A wind blows at a speed of 35 mi/hr 30 degrees west of south. What is the plane's resultant velocity?

Answer 1

Compute the components of the given vectors. Let $P$ denote the plane's velocity vector, and $W$ the wind. Then

$P=\langle P_x,P_y\rangle=\langle250\cos(-40^\circ),250\sin(-40^\circ)\rangle$

$\implies P=\langle191.5,-160.7\rangle$

$W=\langle35\cos(-120^\circ),35\sin(-120^\circ)\rangle=\langle-17.5,-30.3\rangle$

The resultant velocity (rounded) is

$P+W=\langle174,-191\rangle$

with magnitude $\sqrt{174^2+(-191)^2}=258$ and direction $\tan^{-1}\frac{-191}{174}=-47.7^\circ$, or about 258 mi/hr at 47.7 degrees south of east.