Relative Velocity, Aeroplane Problem

[TheRedDevil18]

Homework Statement

An airplane pilot sets a compass course due west and maintains an airspeed of 225km/h . After flying for a time of 0.470h , she finds herself over a town a distance 119km west and a distance 14km south of her starting point.

1) Find the magnitude of the wind velocity.

2) Find the direction of the wind velocity.
Express your answer as an angle measured south of west

3) If the wind velocity is 36km/h due south, in what direction should the pilot set her course to travel due west? Use the same airspeed of 225km/h
Express your answer as an angle measured north of west

Homework Equations

The Attempt at a Solution

I'm stuck at the first one

This is what I tried,

sqrt(119^2 + 14^2) = 120km

120/0.47 = 255km/h

Wind speed = sqrt(255^2 - 225^2)
= 120km/h, which is incorrect, any help ?

 

[Doc Al]

Set up a vector equation:
$$\vec{V}_{plane/ground} = \vec{V}_{plane/air} + \vec{V}_{air/ground}$$