# Vector addition and angle

1. Dec 28, 2015

### David112234

1. The problem statement, all variables and given/known data
Canada geese migrate essentially along a north-south direction for well over a thousand kilometers in some cases, traveling at speeds up to about
100 km/h. The one goose is flying at 100 km/h relative to the air but a 38 km/h -km/h wind is blowing from west to east.
At what angle relative to the north-south direction should this bird head to travel directly southward relative to the ground?
2. Relevant equations
basic vector addition and components , distance formula

3. The attempt at a solution
1 vector E to W 38
1 vector S to N 100
the angle of the resulting vector is arctan 38/100 =20.806 N of E
90-20.806 = 69.19 W of N
How is this not right? this is simple vector stuff which I know well.

2. Dec 28, 2015

### haruspex

You are treating the two as given (applied) vectors and adding them, which gives a resultant.
But here you are given one applied vector (the wind) the magnitude of the other applied vector (bird's speed relative to wind) and the direction of the resultant (desired path relative to ground).

3. Dec 28, 2015

### David112234

I am not sure what you mean, what do you mean by "applied" vector, I am not used to this terminology.

4. Dec 28, 2015

### haruspex

You'd probably be comfortable with calling a force vector an applied vector, but you can also use the concept here. The bird applies a vector by flying at a certain velocity relative to the wind. The wind applies its velocity vector relative to the ground. The resultant (vector addition) is the vector of the bird's motion relative to the ground.

5. Dec 28, 2015

### David112234

So then what was wrong with my approach?

6. Dec 28, 2015

### haruspex

You took the bird's contribution to the vector sum as being 100kph S. It isn't. It is 100kph in a direction to be determined. The resultant of the vector addition is required to be in the S direction.

7. Dec 28, 2015

### SteamKing

Staff Emeritus
You seem to have at least written the directions of these vectors opposite of what the statement above specified.

1) The geese are migrating from the north to the south, not from the south to the north.
2) The wind is blowing from west to east, not east to west.

You should make a simple sketch of the two vectors, which will at least help you to figure the right quadrant into which the resultant falls.

With the geese headed south and the wind blowing from the west, in what direction would the flock be headed before shifting course in order to fly due south?

8. Dec 28, 2015

### Mister T

I have always found an equation of this form to be helpful,

$\vec{v}_{AC}=\vec{v}_{AB}+\vec{v}_{BC},$

along with a vector diagram showing the head-to-tail vector addition.

$\vec{v}_{AC}$ is the velocity of A relative to C.
$\vec{v}_{AB}$ is the velocity of A relative to B.
$\vec{v}_{BC}$ is the velocity of B relative to C.

9. Dec 29, 2015

### David112234

Got it, thanks for the help