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
`√(174^2+(-191)^2)=258` and direction
`\tan^(-1)(-191)/(174)=-47.7^\circ`, or about 258 mi/hr at 47.7 degrees south of east.