Airplane direction and wind direction

[JSan]

Homework Statement

I have an example problem I would like to solve and unsure how to graphically set up the problem. I would like to derive the answer by the component method of deriving vectors instead of law of sines/cosines. An airplane is trying to keep on a due west course towards an airport. The airspeed of the plane is 600 km/hr. If the wind has a speed of 40 km/hr and is blowing at a direction of 30 degrees S of W, what direction should the aircraft be pointed and what will be its speed relative to the ground.

Homework Equations

R=√(R$^{2}$$_{x}$+R$^{2}$$_{y}$)
tanθ=|$\frac{R_{y}}{R_{x}}$|

The Attempt at a Solution

Unsuccessful in setting up problem

 

[jedishrfu]

First try drawing a vector for the wind and one for the plane's intended path (ie west) and one for the planes actual direction and label them with the speeds for each vector.

Ask yourself how do these add together.

 

[CWatters]

There are many types of vector problem...

An easy vector problem would give you two vectors A and B and have you calculate the resultant R.

A slightly harder problem would give you the resultant R, one vector A and ask you to calculate vector B.

In this case you have a combination of both. You are given:

The direction component of the resultant R (West)
The speed and direction of vector A (40 km/hr and 30 degrees S of West)
The velocity component of vector B (600 km/hr)

You need to find the velocity component of R and the direction component of B.

Do what jedishrfu said. Start by making a drawing and mark all the known and unknown variables on it.