# Relative velocity of a plane problem

1. Feb 12, 2010

### zero_infinity

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

2. Relevant equations
Pythagorean theorem?
tan-1(y/x)=theta

3. The attempt at a solution
http://img709.imageshack.us/img709/8219/15610642.png [Broken]
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/h

wtf?

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.

Last edited by a moderator: May 4, 2017
2. Feb 12, 2010

### Gib Z

You should swap the purple and blue vectors; the plane should be travelling 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.

3. Feb 12, 2010

### zero_infinity

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 subtraction

I don't understand what you mean.

4. Feb 12, 2010

### 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.

5. Feb 12, 2010

### zero_infinity

What is wrong with what I am already doing?

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

6. Feb 12, 2010

### Gib Z

Read my post: V_pw is 250, not V_pg.

EDIT: In response to your edit, yes, thats is.