# What Angle Should the Goose Fly to Head Directly Southward?

• David112234
In summary, the angle at which the goose should head to travel directly southward relative to the ground is 20.806 degrees, which is arctan 38/100 of the angle between the geese's migration direction and the direction of the wind.
David112234

## Homework Statement

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?

## Homework Equations

basic vector addition and components , distance formula

## 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.

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).

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

David112234 said:
I am not sure what you mean, what do you mean by "applied" vector, I am not used to this terminology.
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.

haruspex said:
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.
So then what was wrong with my approach?

David112234 said:
So then what was wrong with my approach?
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.

David112234
David112234 said:

## Homework Statement

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?

## Homework Equations

basic vector addition and components , distance formula

## The Attempt at a Solution

1 vector E to W 38
1 vector S to N 100

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.

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.

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?

David112234
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.

Thewindyfan and David112234
Got it, thanks for the help

## 1. What is vector addition and how is it done?

Vector addition is the process of combining two or more vectors to create a new vector. It involves adding the magnitudes of the vectors in the same direction and taking into account their direction. This can be done graphically by placing the vectors head-to-tail or mathematically by adding their components.

## 2. What is the difference between vector addition and scalar addition?

Vector addition involves adding both the magnitude and direction of vectors, while scalar addition only involves adding their magnitudes. Scalar addition is represented by simple addition, while vector addition requires more complex calculations and considerations of direction.

## 3. How do you calculate the angle between two vectors?

The angle between two vectors can be calculated using the dot product formula: cosθ = (a · b) / |a||b|, where a and b are the two vectors and |a| and |b| are their magnitudes. This will give the cosine of the angle between the vectors, which can then be solved for θ using inverse trigonometric functions.

## 4. Can vectors be added or subtracted if they are not in the same direction?

Vectors can only be added or subtracted if they are in the same direction. If they are not, they must first be resolved into their components in the same direction before being added or subtracted. This can be done by using trigonometric functions to find the magnitude and direction of the components.

## 5. How is the result of vector addition represented?

The result of vector addition is represented by a new vector, often shown with an arrow pointing from the tail of the first vector to the head of the last vector. The magnitude and direction of the resulting vector can be calculated using trigonometric functions or by measuring on a graph.

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