Relative velocity of a plane problem

[zero_infinity]

Homework Statement

a plane flies at an airspeed of 250 km/h. A wind is blowing at 80 km/h toward the direction 60(degrees) east of north.

a) in what direction should it fly in order to fly north relative to the ground?
b) what is the speed of the plane relative to the ground?

Homework Equations

Pythagorean theorem?
tan^-1(y/x)=theta

The Attempt at a Solution

http://img709.imageshack.us/img709/8219/15610642.png
the back of the book states:
a) 16 west of north
b) 280 km/s (i think it means km/h)

i get
a) 108 (18 west of north)
b) 221 km/hwtf?now that i look over it, I'm not really sure where the 250 goes. If the plane travels at 250 km/h and the wind also it pushes north-east, then it should be going faster.

 

[Gib Z]

You should swap the purple and blue vectors; the plane should be traveling in the current blue direction to compensate for the wind and achieve an overall north motion.

Also, the red vector should only have the arrow pointing in the north eastish direction, and should stop on the vertical axis.

 

[zero_infinity]

You should swap the purple and blue vectors; the plane should be traveling in the current blue direction to compensate for the wind and achieve an overall north motion.

Also, the red vector should only have the arrow pointing in the north eastish direction, and should stop on the vertical axis.

right... it has to fly in the blue direction to compensate for the wind. It's asking you to find that direction and speed. Why do the vectors have to be switched? It has to fly north relative to the ground so that has to be the vector relative to the ground.

i extended the red vector to show subtractionI don't understand what you mean.

 

[Gib Z]

Sorry I seem to have just misunderstood your notation.

Ok so you know V_pw = 250, V_wg = 80, and the angle V_wg makes with the vertical axis is 60 degrees since the angle sum of a straight line is 180 degrees. So now you have a triangle with two known sides and a known angle; with the sine and cosine rules you can figure everything about the triangle now.

 

[zero_infinity]

Sorry I seem to have just misunderstood your notation.

Ok so you know V_pw = 250, V_wg = 80, and the angle V_wg makes with the vertical axis is 60 degrees since the angle sum of a straight line is 180 degrees. So now you have a triangle with two known sides and a known angle; with the sine and cosine rules you can figure everything about the triangle now.

What is wrong with what I am already doing?

250 is supposed to be the V_pw vector? that's it?

 

[Gib Z]

Read my post: V_pw is 250, not V_pg.

EDIT: In response to your edit, yes, that's is.