Let
be the velocity of the plane.let
be the velocity of the wind.let
be the resultant velocity.add the velocities to find the resultant velocity. in the attached picture, i have done the tail-to-tip method: draw one of the vectors, then add the end of the other vector to the tip of the first drawn vector.see diagram.the magnitude of
can be found via the pythagorean theorem as this is a right angle triangle.
to find
, use inverse tangent:
since
is in the direction "east of north", a quick convert to "north of east " reveals that 90 - 7.06 = 82.94 = 83.so our resultant is 529 m/s [83° n of e]the answer is a.