An aircraft pilot wishes to fly from an airfield to a point lying S20oE from the airfield. There is a wind blowing from N80oE at 45 km/h. The airspeed of the plane will be 550 km/h.

Question

(a) What direction should the pilot steer the plane (to whole degree)? Include a diagram as part of your solution.

(b) What will the actual ground speed be of the plane (to one decimal place)?

Answer 1

Draw a diagram. It should be clear that the angle between the wind's direction (measured counter-clockwise) and the desired course is 100°

Doing part (b) first, using the law of cosines you can see that the plane's ground speed s can be found using
550^2 = 45^2 + s^2 - 2*45s*cos100°
s = 540.4
This makes sense, since the wind is a small headwind, slowing down the plane.

Now, using the law of cosines to find the angle θ between the wind and the plane's course,
540.4^2 = 45^2 + 550^2 - 2*45*550 cosθ
cosθ = 0.25238
θ = 75.38°
We subtract the 10° angle of the wind, and the resultant course of the plane is E65.38°S
That is, S24.6°E, slightly east from the desired course, due to the headwind.

Answer 2

thank you sooo much

Answer 3

wait why did u subtract 10 degrees? where does the 10 degrees come from?
at the end