Relative Motion of a plane in a storm

[retracell]

Homework Statement

The navigator of an airplane plans a flight from one airport to another 1200km away, in a direction 30 degrees east of north. The weather office informs him of a prevailing wind from the west, of 80km/h. The pilot wants to maintain an air speed of 300km/h.

What heading should the navigator give the pilot?

Homework Equations

Basic kinematic and relative motion equations. eg. v=dt

The Attempt at a Solution

I tried drawing many different triangles regarding the heading of the plane and the direction of travel. I got to two equations, something like:

tan30 = (Vx+80)/Vy
Vx^2 + Vy^2 = 300^2

If this is right, I was wondering if there was a simpler way.

 

[SeanGillespie]

It is solved by using vectors. The best way to simplify it is by drawing a triangle. If the pilot flew straight towards the airport at 300km per hour they would end up east of the airport due to the eastward wind.

The pilot would need to fly at an angle towards the northwest to overcome the cross wind. You need a right angle triangle where the air speed is the adjacent to the angle of travel and the speed of the wind is the side opposite the plane's heading. You should be able to find the angle using tan.

These questions can be confusing though, so if you have the answer at hand try changing the side which has the airspeed to the hypotenuse and recalculate the angle.

I got in a muddle with a similar question a number of weeks ago, and to be honest, I've forgot the correct solution already.