# Placements of vector diagrams and angles in 2-D collisions

• JohnMC
In summary, the conversation discusses the confusion and difficulty the person is having with two-dimensional collisions, specifically with vector positions and theta angles. They mention their attempts to understand and decipher the book's placement of diagrams and use of rulers and protractors, and how they believe their own arrangement may be less confusing. The conversation also touches on the purpose of using a ruler and protractor, and the importance of analyzing each problem individually and being able to recognize correct solutions even if they are not approached in the same way.
JohnMC

## Homework Statement

Regarding two-dimensional collisions, I just don't understand why my book suddenly changes vector positions and theta angles at different places than what I was accustomed to. I understand that they're getting me to think by changing questions and answers, but I'm confused WHY they placed it there. My important queries and comments are in the photo links that are bolded and the other links are just for context. Also, I have decided not to post more pictures for continuation in Question #1 because the next steps are irrelevant.

QUESTION #1
STEP I. http://img686.imageshack.us/img686/938/41145645.jpg
STEP II. http://img198.imageshack.us/img198/9696/65034028.jpg
STEP III. http://img39.imageshack.us/img39/677/66356214.jpg
STEP IV. http://img198.imageshack.us/img198/4056/91707666.jpg

QUESTION #2
STEP I. http://img64.imageshack.us/img64/4439/20331196.jpg
STEP II. http://img198.imageshack.us/img198/1593/58858513f.jpg

N/A

## The Attempt at a Solution

Attempted to "decipher" the question in hopes of why the book placed it there, but to no avail. It could be the wording, though, but I don't see anything. Forgive me for posting because it's hard being taught only from the book with no other sources of help other than physicsforums.com

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JohnMC said:
QUESTION #1
STEP I. http://img686.imageshack.us/img686/938/41145645.jpg
STEP II. http://img198.imageshack.us/img198/9696/65034028.jpg
STEP III. http://img39.imageshack.us/img39/677/66356214.jpg
STEP IV. http://img198.imageshack.us/img198/4056/91707666.jpg

Your arrangement (Step IV) is not different from the book's arrangement in Step III.

Step III says that
-pCf = pAf + pBf

Step IV says that
-pCf = pBf + pAf

In other words, if you start at the tip of vector pCf and go first to the left and then down (Step III) you end up at the origin the same as if you went down first and then to the left (Step IV). Vector addition is commutative, it makes no difference which term comes first and which comes second when you add vectors.

However, the book's way of showing the diagram (Step III) makes it necessary to place the angle outside the triangle so that it becomes obvious to the reader that the direction of vector is 50o (or whatever) "North of East". If they placed the angle inside the triangle, it would not be as obvious. Of course, you way of drawing the same thing (Step IV) takes care of the problem automatically. So, in retrospect, I would say that your way of showing what is going on is less confusing.

I am not sure why the book asks you to use a ruler and a protractor. Maybe to reinforce the idea that trig functions can be obtained by taking ratios of sides of a right triangle instead of pushing buttons on one's calculator. Just a guess.

QUESTION #2
STEP I. http://img64.imageshack.us/img64/4439/20331196.jpg
STEP II. http://img198.imageshack.us/img198/1593/58858513f.jpg

Although you don't show exactly what the question is, it obviously has to do with momentum conservation in two dimensions. You need to write all vectors involved as vectors and them add them vectorially to get the answer. That's the purpose of the part you think you don't need.

I don't see how the vector diagram can be placed in the third quadrant. Because vector pBf points "East", the vector diagram must be placed in the first quadrant or the fourth, if you displaced the whole thing down by an amount equal to the magnitude of pAf.

I don't think anyone is trying to confuse you. Each situation needs to be analyzed on its own merits and there are many different ways to approach a physics problem, all of them correct. The trick is to be able to see that a solution is correct even if it is not the way you would do it.

Last edited by a moderator:
.

As a scientist, it is important to understand that textbooks and resources may present information in different ways in order to challenge your understanding and critical thinking skills. In the case of vector diagrams and angles in two-dimensional collisions, it is likely that the book is trying to present the information in a different format to help you better understand the concept. It is important to focus on the underlying principles and equations rather than the specific placement of diagrams and angles. If you are having trouble understanding the reasoning behind the placement, it may be helpful to seek additional resources or ask your teacher for clarification. Keep in mind that there may be multiple ways to approach and solve a physics problem, and it is important to be open to different perspectives and methods.

## 1. How do you determine the placement of vector diagrams in 2-D collisions?

The placement of vector diagrams in 2-D collisions is determined by the direction and magnitude of the vectors involved. The vectors should be drawn in the same direction as the motion of the objects and their lengths should represent the relative speeds of the objects.

## 2. What is the purpose of using vector diagrams in 2-D collisions?

The purpose of using vector diagrams in 2-D collisions is to visually represent the velocities and directions of the objects involved in the collision. This can help in understanding the dynamics of the collision and predicting the outcome.

## 3. How are angles measured in 2-D collision vector diagrams?

In 2-D collision vector diagrams, angles are measured counterclockwise from the positive x-axis. This convention allows for easier comparison and calculation of angles between different vectors.

## 4. Can vector diagrams be used for both elastic and inelastic collisions?

Yes, vector diagrams can be used for both elastic and inelastic collisions. In elastic collisions, the total kinetic energy is conserved and the vectors drawn will show the same magnitude and direction before and after the collision. In inelastic collisions, some kinetic energy is lost and the vectors will show a change in magnitude and direction.

## 5. How do you calculate the final velocity of an object in a 2-D collision using vector diagrams?

The final velocity of an object in a 2-D collision can be calculated by adding the x and y components of the vectors involved in the collision. This can be done using trigonometric functions and the Pythagorean theorem.

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