To end up due north, the pilot will need to fly the plane how many degrees west of North

Question

an airplane needs to head due north but there is a wind blowing from the southwest at 80 km/hR the plane flies at an air speed of 650 km / h r

Answer 1

This is a problem in vector analysis. We want to add two velocity vectors so that the resultant vector is directed due north. We know that the wind is blowing at a velocity of 80 km/hr in the northeast direction (from southwest), and we also know that the plane travels with a velocity of 650 km/hr.

The northeast direction is 45° to the east of north (clockwise from north), so the only thing we have left to do is determine the angle the direction of the plane makes with due north. In order for the plane to have a resultant velocity vector directed due north the plane must angle itself west of north by just enough to offset the crosswind.

The east/west component of the wind velocity vector is found by

v_{wind, E/W} = v_wind * sin(45°)

= (80 km/hr) * (0.71)

= 5.7 km/hr.

Now we know that the E/W component of the planes velocity must counter that by tilting through an angle θ such that

sin(θ) = (E/W component of plane's velocity) / (flight velocity)

= (5.7 km/hr) / (650 km/hr).

Now we can take the inverse sine of both sides to find θ to be (in degrees)

θ = 0.50°.