Question

An airplane is travelling at a speed of 600 mph on a heading of 345 degrees. There is a wind moving at a speed of
70 mph on a heading of 20 degrees. The pilot would like to maintain his planned course. Find the speed and heading he should set in order to travel with the wind and keep on course.
bobpursley
so his his heading + wind=345

let Theta be his heading steered.
600sinTheta W + 600cosTheta E + 70 sin20 E + 70 cos 20 N=SOG*sin345 W + SOG cos345 N
(SOG is speed over grund)

set the components equal
West: 600 sinTheta W+70cos20 E=sog sin345 W
or
change the second direction E to -W, solve for Theta.
Put that into the N equation to solve for SOG.

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