# Calculating vector components (displacement, oooh)

• ellal
In summary, Sophie's displacement is 412.3 M [W 14 degrees N] and her average velocity is 16.5 M/min [W 14 degrees N]. In order to calculate this, the Pythagorean theorem was used to break down the 400 M [SE] into its south and east components, and the angle was determined to be 45 degrees. This corrected calculation takes into account the fact that 400 m south east is not the same as 400 m south then 400 meters east.
ellal

## Homework Statement

Sophie walks 800 M [N], then 500 M [W] and finally 400 M [SE] in 25 minutes. What is her displacement and average velocity? (Using scale diagram)

a2 + b2 = c2

## The Attempt at a Solution

I tried calculating by creating separate triangles, but was not certain what to do with the 400 M [SE] as I was not given an angle.

This was my attempt, assuming that both south and east are 400 M

Y = 800 north - 400 south = 400 M north
X= -500 or 500 west + 400 east = -100 or 100 west

Using Pythagorean theorem, I calculated for size Z and got 412.3 M
Then moving forward from that to calculate the direction, I said tan-1 (100/400) equals 14 degrees.

My final answer was 412.3 M [W 14 degrees N]

Now I also do not have an answer key and this is an assignment that I can't figure out. Any help would be appreciated, thank you!

You do have the angle for 400 m [SE]. They mean she was traveling EXACTLY south east. That direction is 45 degrees from south and 45 degrees from east.

You made another mistake. 400 m south east is not the same as 400 m south then 400 meters east. You need to use the pythagorean to break 400 m [SE] into south and east components.

flatmaster said:
You do have the angle for 400 m [SE]. They mean she was traveling EXACTLY south east. That direction is 45 degrees from south and 45 degrees from east.

You made another mistake. 400 m south east is not the same as 400 m south then 400 meters east. You need to use the pythagorean to break 400 m [SE] into south and east components.

I just tried it and it makes much more sense now! Thanks again!

## 1. What is a vector component?

A vector component is a part of a vector that is parallel to one of the axes of a coordinate system. It is represented by a number and a direction.

## 2. How do you calculate vector components?

To calculate vector components, you can use the trigonometric functions sine and cosine. The x-component of a vector is equal to the magnitude of the vector multiplied by the cosine of the angle it makes with the x-axis. The y-component is equal to the magnitude of the vector multiplied by the sine of the angle.

## 3. What is the difference between displacement and distance?

Displacement is a vector quantity that represents the change in position of an object from its initial position to its final position. Distance, on the other hand, is a scalar quantity that represents the total length of the path traveled by an object.

## 4. How do you calculate displacement using vector components?

To calculate displacement using vector components, you can use the Pythagorean theorem. The magnitude of the displacement is equal to the square root of the sum of the squares of the x and y components.

## 5. Can you have negative vector components?

Yes, vector components can be negative. The direction of a vector component is determined by the coordinate system in which it is being represented. If the vector is pointing in the negative direction of an axis, its component in that direction will also be negative.

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