An airplane is flying at 400 km/h on a heading of 050°. The wind is blowing at 30 km/h at a bearing of 153°. Determine the ground velocity of the airplane and the direction of flight.

Answer 1

Vectorizing:

A = 400 cos(50°)i+400sin(50°)j = A_xi+A_yj

W = 30 cos(153°)i+30sin(153°)j = W_xi+W_yj

A+W = (A_x+W_x)i + (A_y+Wy)j = G_xi+G_yj

Ground velocity,G = |A+W| = √((G_x)²+(G_y)²)

direction = tan^-1(G_y/G_x)