Question

A new passenger airplane is flying from Vancouver heading overseas to Asia. The wind is blowing from the west at 90 km/h. The airplane is flying at a speed of 950 km/h and must stay on a heading of south 60 degrees west
A) What heading should the pilot take to compensate for the wind?
B) What is the speed of the airplane relative to the ground?

Answer 1

He must stay on a course of S 60 W. We must find the heading :)
h is degrees heading west of south

say his speed over the ground is s
then west speed over ground
= s sin 60 = 950 sin h - 90
and south speed over ground
= s cos 60 = 950 cos h

so
.866 s = 950 sin h - 90
.5 s = 950 cos h

work with that

Answer 2

.866 s = 950 sin h - 90
.866 s = 1645 cos h
---------------------subtract
950 sin h = 1645 cos h + 90
or
950 sin h - 1645 cos h = 90
for various values of h
h , left side
60 , .224
61 , 33.4
62 , 66.5
63 , 99.6 so steer 62.5 degrees west of south
65 , 165
70 , 331

Answer 3

I will leave you to get s now