An aircraft travels at 250km/h in still air. If a wind of 50km/h blows steadily from the southwest and the pilot wishes to fly due north, find the course he must set and the ground speed of the aircraft. On the return journey the wind speed and direction are unaltered. Find the new course and ground speed.

Answer 1

As with all geometry and related problems, the first step is to draw a triangle of velocities.

Wind is from south-west at 50 km/h.
Draw a line from A to B with an arrow pointing north-east. From B, draw a line (approx. 5 times as long) towards north, ending at C which is exactly north of A.
So we have an oblique triangle ABC, with angle A=45 degrees, AB=50, BC=250.
Solve by sine-rule,
sin(A)/BC=sin(C)/AB, or
sin(C)=sin(A)*AB/BC
=sqrt(2)/2*(50/250)
=.14142
and =>
A=8.1301°
and
B=180-(A+C)=126.8699°
Hence apply the sine rule again to get
AC=sin(B)*BC/sin(A)
=sin(126.8699)*250/sin(45)
=282.843 km

You can proceed similarly for the return trip, and I'll leave that to you. If you encounter difficulties, feel free to post what you have done and we'll take it from there.