Question

An airplane pilot wishes to fly due west. a wind of 80.0 km> h (about 50 mi > h ) is blowing toward the south. (a) if the airspeed of the plane (its speed in still air) is 320.0 km> h (about 200 mi> h ), in which direction should the pilot head?

Answer 1

let the plane is flying at some angle theta with west towards north

Now we can use the components

$v_y = 320 sin\theta$

$v_x = 320 cos\theta$

now since plane has to fly towards west so net speed in north must be equal to speed in south for air

So we can say

$320 sin\theta = 80$

$sin\theta = \frac{1}{4}$

$\theta = 14.5 degree$

so plane has to fly in direction 14.5 degree North of west