# Relative Velocity, Aeroplane Problem

1. Mar 2, 2014

### TheRedDevil18

1. The problem statement, all variables and given/known data

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.

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

2. Relevant equations

3. 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 ?

2. Mar 2, 2014

### Staff: Mentor

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