Answer:
Vs = -400 j speed of plane in still air
Vw = 100 i speed of wind encountered
V = Vs + Vw vector speed of speed respect to ground
V = 100 i - 400 j vector speed of plane
V = (100^2 + 400^2)^1/2 = 412 mph measured speed of plane
tan θ = Vy / Vx = -400 m/ -100 = 4
θ = 76 deg Plane flies southwest (straight south is 90 deg)
Assuming an easterly wind is blowing from the east as specified by weather