airplane problem?

Question

An airplane pilot wishes to fly due west. A wind of 90.0 km/h is blowing toward the south.

If the airspeed of the plane (its speed in still air) is 310.0 km/h, in which direction should the pilot head?
What is the speed of the plane over the ground?

Answer 1

Assuming that the max speed of the plane in still air is Vmax=310.0 km/h we can proceed.

Vmax= Vwest + Vwind(south) (this is a vector equation)
Then Vwest=sqrt( (Vmax )^2 - (Vwind(south)) ^2)
Direction mostly west and just a little bit north

Angle = arcsin(Vwind(south) /Vmax) or assuming that a northern heading is 00 degrees then
it has to fly a heading 360- Angle