# Adding vector components in two dimensions

• Square1
In summary, the plane flies 534 km/h south after encountering a southwestern wind of 100 km/h. The heading is 7.61 degrees.
Square1

## Homework Statement

A plane flies 600km/h south. The plane encounters a southwestern wind of 100km/h.

## Homework Equations

What is the velocity (magnitude and direction) of the plane

## The Attempt at a Solution

What I did was break the 100km southwestern vector into its components. 100*cos45 = 70.71 (45 because southwestern wind is 45deg?). This will be both north and east component since it is 45 45 90 triangle that is being used.

Then I subtract 70.71 north component from 600 original vector = 529.29
Using the new 529.29 south component, and the remaining east pointing 70.71 component, I use phythagoras to find the resulting velocity vector.
I get 534. Answer is 543.

As for the heading, I get 7.61deg, which is inline with the answer.

Square1 said:

## Homework Statement

A plane flies 600km/h south. The plane encounters a southwestern wind of 100km/h.

## Homework Equations

What is the velocity (magnitude and direction) of the plane

## The Attempt at a Solution

What I did was break the 100km southwestern vector into its components. 100*cos45 = 70.71 (45 because southwestern wind is 45deg?). This will be both north and east component since it is 45 45 90 triangle that is being used.

Then I subtract 70.71 north component from 600 original vector = 529.29
Using the new 529.29 south component, and the remaining east pointing 70.71 component, I use phythagoras to find the resulting velocity vector.
I get 534. Answer is 543.

As for the heading, I get 7.61deg, which is inline with the answer.

I googled "plane flies in south direction..etc" for similar questions though, and I find on two websites that I still can't get matching answers.
ex: http://www.jiskha.com/display.cgi?id=1254021349

Square1 said:
I googled "plane flies in south direction..etc" for similar questions though, and I find on two websites that I still can't get matching answers.
ex: http://www.jiskha.com/display.cgi?id=1254021349
Not sure what you are saying. Do you mean that you submitted an answer to the question there and were told your answer is wrong?

No no just that i tried googling that particular question assuming its a "stock question" and people have asked it in the past. I still don't get the same answer as people that have tried to help others on other websites.

Square1 said:
No no just that i tried googling that particular question assuming its a "stock question" and people have asked it in the past. I still don't get the same answer as people that have tried to help others on other websites.
Well, the first answer to the question at that link was wrong. It took the wind as from NE instead of SW, so got an answer greater than 515, which is clearly impossible.

Oh yea... haha...

Ok well...hopefully was a typo...534...543...thank you.

## What is a vector?

A vector is a mathematical representation of a quantity that has both magnitude and direction. It is commonly represented by an arrow, with its length representing the magnitude and its direction representing the direction.

## How do you add vector components in two dimensions?

To add vector components in two dimensions, you must first break down the vectors into their x and y components. Then, you can add the x components together and the y components together to get the resulting vector in two dimensions.

## What is the Pythagorean theorem used for in vector addition?

The Pythagorean theorem is used to calculate the magnitude of the resulting vector when adding two vectors in two dimensions. It states that the square of the length of the hypotenuse (resulting vector) is equal to the sum of the squares of the lengths of the other two sides (individual vector components).

## Can vectors be added in any order?

Yes, vectors can be added in any order as long as their components are added correctly. This is because vector addition is commutative, meaning the order in which the vectors are added does not change the result.

Vector addition involves adding two or more vectors together, taking into account their direction and magnitude. Scalar addition, on the other hand, involves adding two or more quantities that have only magnitude, such as numbers.

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