Question

An airplane has airspeed of 724 k/h at bearing of North 30 degrees East. If the wind velocity is 32 from west. find the ground speed and direction of plane.

Teacher gives solution of 740.5 k/hr and 57.9 degrees.
Can anyone show steps?

Answer 1

convert headings (not bearings!) to x-y coordinates and add them up:

724@30° = (362,627)
32@90° = (32,0)
addthem up and you have
(394,627)
√(394^2+627^2) = 740.5
90-arctan(627/394) = 32.2°
Note that the proposed solution of 57.9° is measured from the x-axis, so it is not a true compass heading.