In still air, an airplane is flying at 100 mph. It encounters a wind blowing toward the west at 50 mph. What should be the plane's compass heading for its course to be N30ºW?

Answer 1

If the plane is flying on heading NθE, then we want

100sinθ-50 = -v/2
100cosθ = v √3/2

100sinθ = 50-v/2
100cosθ = v√3/2

(50-v/2)^2 + 3/4 v^2 = 100^2
v = 115.14

So, cosθ = .997
θ = 4.3º

and the heading is N4.3ºE

Answer 2

Could you explain the (50-v/2)^2 + 3/4v^2 = 100^2 part? I'm a little confused.

Answer 3

square the previous equations and add them up. Recall that

sin^2θ + cos^2θ = 1