# Adding & Subtracting Vecots And Relative Velocity

• rossverg
In summary, when adding or subtracting vectors, it is important to keep in mind that they have both a magnitude and a direction, and that the location of the origin is not important. To add or subtract vectors, simply substitute one vector for another with the same magnitude and direction, and use the parallelogram law of addition. When dealing with relative velocity, the formula given can be used, but it is important to remember that it is referring to the components of the vectors in the chosen axis system, and not the actual vectors themselves. It is also possible to use vector diagrams to solve these problems. The correct way to solve for relative velocity is to subtract the x- and y-components of the vectors and use the Pythagorean The
rossverg
Adding & Subtracting Vectors And Relative Velocity

Hey everyone, I am so confused with this it's not funny. This is my first time accessing a site like thisss, but I am desperate seeing as though it's school holidays atm where I am and I can't talk to my physics teacher for help. Anyhow, I hope one of you guys can help me out.

Ok I have 2 problems.

One is with adding and subtracting vectors. Ok when I have to vectors to add or subtract say

12ms-1 west + 14 ms-1 north

<IMG SRC="http://members.optushome.com.au/rossverg2002/1.JPG">

Before I do anything I draw my diagram as descbried above. The problem is that in oder to add them I need to have the vectors touching arrow-to-tail. The problem is which one of the arrows do I reverse and how do I express the new velocity (with a - sign?). Does it even matter which arrow (velocity and direction) I reverse?

Ok second problem ... I am confused with relative velocity. In my textbook there is a formula:

Velocity of a relative to b = velocity of a - velocity of b.

How do I know when to use the formula or vector diagrams? Is it only meant for velocities in a straight line? What do I do when there are 2 dimensional velcoities (like a velocity north relative to a velocity east); do I use vector diagrams instead of teh formula??

Here is an example I am stuck on with the above problem.

Car A travels at a velocity of 30.5 ms-1 north while car B travels at a velocity 25 ms-1 east. What is the velocity of B relative to A?

If I use the formula, I get 55.5 ms-1. (Velocity of b rel to a = 25 - (-30.5) which = 55ms-1)

If I use a vector diagram and find the velocity via pythagoras, I get 39.44 ms-1 N34degreesW.

Which way is the right way?? :S:S:S

Thankyou to all who help.
Your help is greatly appreciated.

#### Attachments

• 1.JPG
1.1 KB · Views: 388
Last edited by a moderator:
rossverg said:
Hey everyone, I am so confused with this it's not funny. This is my first time accessing a site like thisss, but I am desperate seeing as though it's school holidays atm where I am and I can't talk to my physics teacher for help. Anyhow, I hope one of you guys can help me out.

Ok I have 2 problems.

One is with adding and subtracting vectors. Ok when I have to vectors to add or subtract say

12ms-1 west + 14 ms-1 north

<IMG SRC="http://members.optushome.com.au/rossverg2002/1.JPG">

Before I do anything I draw my diagram as descbried above. The problem is that in oder to add them I need to have the vectors touching arrow-to-tail. The problem is which one of the arrows do I reverse and how do I express the new velocity (with a - sign?). Does it even matter which arrow (velocity and direction) I reverse?

First, vectors have two important characteristics. They have a magnitude and they have a direction. The location isn't that important. If two vectors start from different origins, but have the same direction and magnitude, then they are equal.

Going back to basic algebra:

If A=B, and A+C=D, then what does B+C=? Obviously it equals D.

Since the origins of your two vectors occupy the same spot, they're not set up to add together very well. Instead, you simply substitute in a new vector at the location you need that has the same magnitude and direction as one of your vectors. (In other words, you don't reverse the direction of either vector).

Addition is commutative, so you don't care which vector you move (or, technically, substitute). You can add the vectors in either order.

Try it both ways. You'll find you've created a parallelogram (a rectangular parellelogram for the example you gave). The sum equals the diagonal of the parallelogram either path you take. (That's why it's sometimes called the parallelogram law of addition).

Last edited by a moderator:
rossverg said:
Ok second problem ... I am confused with relative velocity. In my textbook there is a formula:

Velocity of a relative to b = velocity of a - velocity of b.

How do I know when to use the formula or vector diagrams? Is it only meant for velocities in a straight line? What do I do when there are 2 dimensional velcoities (like a velocity north relative to a velocity east); do I use vector diagrams instead of teh formula??

Here is an example I am stuck on with the above problem.

Car A travels at a velocity of 30.5 ms-1 north while car B travels at a velocity 25 ms-1 east. What is the velocity of B relative to A?

If I use the formula, I get 55.5 ms-1. (Velocity of b rel to a = 25 - (-30.5) which = 55ms-1)

If I use a vector diagram and find the velocity via pythagoras, I get 39.44 ms-1 N34degreesW.

Which way is the right way?? :S:S:S

Thankyou to all who help.
Your help is greatly appreciated.
The second is the correct answer, almost. I think you made a typo on the direction, since it's 39.34 degrees West of North (N39W).

You misinterpreted what they meant by the formula. If North is your positive x-axis (prinicipal direction) then east is your positive y-axis.

Vector A = [30.5 , 0]. Vector B = [0 , 25].

You subtract by components: Subtract the x-components from each other, subtract the y-components from each other to get a new vector.

In other words, the new vector is [30.5-0 , 0-25], which equals [30.5, -25]

You use the Pythagorean Theorem to find the magnitude and the tangent to find the direction.

You may find this discussion of vector addition helpful: http://www.glenbrook.k12.il.us/gbssci/phys/Class/vectors/u3l1b.html

Last edited by a moderator:
Thanks Bob G so much for clearlying that up.
I've got a much clearer picture of what this is all about now.

Thanks DocAl for that link as well. :)

## 1. What are vectors and how are they added and subtracted?

Vectors are mathematical quantities that have both magnitude (size) and direction. They are typically represented by arrows, with the length of the arrow representing the magnitude and the direction pointing towards the direction of the vector. To add or subtract vectors, we use the head-to-tail method. This involves placing the tail of one vector at the head of the other and drawing a new vector from the tail of the first to the head of the second. The resulting vector is the sum or difference of the original vectors, respectively.

## 2. What is relative velocity and how is it calculated?

Relative velocity is the velocity of an object in relation to another object. It takes into account the motion of both objects and is calculated by subtracting the velocity of the second object from the velocity of the first object.

## 3. How do we handle vectors in different coordinate systems?

Vectors can be represented in various coordinate systems, such as Cartesian, polar, or spherical coordinates. To add or subtract vectors in different coordinate systems, we first need to convert them to the same coordinate system. This can be done using trigonometric functions and basic geometry.

## 4. Can vectors be multiplied or divided?

Vectors cannot be multiplied or divided in the traditional sense. However, there are two types of vector multiplication: dot product and cross product. The dot product of two vectors results in a scalar quantity, while the cross product results in a vector that is perpendicular to both original vectors.

## 5. How is the concept of relative velocity used in real life?

The concept of relative velocity is used in many real-life scenarios, such as in navigation, air traffic control, and sports. For example, an airplane's velocity in relation to the ground is its relative velocity, which is important for determining its flight path and arrival time. In sports, relative velocity is used to determine the speed of a ball in relation to the player's motion, which can help improve performance.

• Introductory Physics Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
25
Views
1K
• Introductory Physics Homework Help
Replies
20
Views
994
• Introductory Physics Homework Help
Replies
3
Views
497
• Introductory Physics Homework Help
Replies
16
Views
752
• Introductory Physics Homework Help
Replies
21
Views
287
• Introductory Physics Homework Help
Replies
56
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
797
• Introductory Physics Homework Help
Replies
7
Views
1K
• Introductory Physics Homework Help
Replies
6
Views
933