An airplane is flying on a bearing of 265° at 420 mph. a wind is blowing with a bearing of 210° at 30 mph. find the actual speed and direction of the plane.

In both cases, y and x components are solved and added. The resulting hypotenuse is then computed and its direction calculated.

Airplane:

Ф = 270 - 265 = 5°

Hypotenuse, h = 420 mph

y component = 420 Sin Ф = 420 Sin 5 = 36.61 mph

x component = 420 Cos Ф = 420 Cos 5 = 418.40 mph

Wind

Ф = 270 - 210 = 60°

Hypotenuse, h = 30 mph

y component = 30 Sin 60 = 25.98 mph

x component = 30 Cos 60 = 15 mph

Total y = 36.61+25.98 = 62.59 mph

Total x = 418.40+15 = 433.40 mph

Resulting speed of airplane = Sqrt (y^2+x^2) = Sqrt (62.59^2+433.40^2) = 437.9 mph

Direction = 270 - [tan^-1 (y/x) ] = 270 - [tan^-1 (62.59/433.40) ] = 261.78°