The velocity of an airplane with respect to the air is 250mph with a bearing of N60 E..?

Question

The wind's velocity 20mph and is blowing north. What is the resultant speed and direction of the plane with the respect to the ground?

Answer 1

Let AB represent the plane's airspeed, and BC represent the wind.

Angle ABC = 180 - 60 = 120 deg.

The resultant is:

AC = sqrt[ 250^2 + 20^2 - 2 * 250 * 20 cos(120) ]

= 261 mph.

sin(BAC) / 20 = sin(120) / AC

BAC = 3.8 deg.

The direction of AC is:

N (60 + 3.8) E

= N 63.8 E.