An airplane is traveling 725 m/s at 48.8° degrees north of west when a wind starts to blow. The velocity of the wind is 106.7 m/s and it is blowing 21.8° east of north. What is the speed of the airplane relative to the ground?

Answer 1

Vp = 725m/s[W.48.8oN] + 106.7[E68.2N] =
-725*Cos48.8+725*sin48.8 + 106.7*Cos68.2
+106.7*sin68.2 = -478+546i + 39.6+99.1i = -438.4 + 645.1i = 780m/s[W55.8oN] =
780m/s[N34.2oW].

Answer 2

Unless otherwise indicated, all angles are measured CCW from +x-axis.

Vr = 725m/s[131.2o] + 106.7m/2[68.2o].

X = 725*Cos131.2 + 106.7*Cos68.2= -438 m/s.

Y = 725*sin131.2 + 106.7*sin68.2 = 645 m/s.

Tan A = Y/X = 645/-438 = -1.47162.
A = 55.8o N. of W.

Vr = Y/sin A = 645/sin55.8 = 780 m/s.
= Resultant velocity.