# Vector Problem -- Addition of two vectors given in polar coordinates

• randomphysicsguy123
In summary, someone provided a figure from a free online SAT Physics site that was not from an SAT prep book. They are asking if they did it right and if not what did they do wrong and how to correct it.
randomphysicsguy123
Homework Statement
Find the resulting vector
Relevant Equations
c^2=a^2+b^2
Doing a review for my SAT Physics test and I'm practicing vectors. However, I am lost on this problem I know I need to use trigonometry to get the lengths then use c^2=a^2+b^2. But I need help going about this.

Last edited by a moderator:
What do you know about vector components?

Note that you have to make an effort yourself.

I have made an effort however I am unsure if my first step of 10sin(70) and 8tan(45) is correct as I do not want to go off track from the start

randomphysicsguy123 said:
I have made an effort however I am unsure if my first step of 10sin(70) and 8tan(45) is correct as I do not want to go off track from the start
It's hardly a long, extended problem. You have to post what you've done.

Note that ##10\sin(70)## by itself is just a number. What do you intend to do with that number?

Work:
x=10cos70=3.4

x=8cos45=5.65

y=10sin70=9.3

y=8sin45=5.65

x(hat)=3.4+5.65=9.05

y(hat)=9.3+5.65=14.95

R=sqrt(9.05^2+14.95^2)=17.47

R=17.47

randomphysicsguy123 said:
Work:
x=10cos70=3.4

x=8cos45=5.65

y=10sin70=9.3

y=8sin45=5.65

x(hat)=3.4+5.65=9.05

y(hat)=9.3+5.65=14.95

R=sqrt(9.05^2+14.95^2)=17.47

R=17.47
I'll try to look through that in a bit, but a couple of suggestions:

** Please check out the LaTeX Guide at the lower left of the Edit window. That's the best way to post math equations at the PF and many other websites

** It would help if you commented each line that you posted. Presumably you are resolving the two vectors into rectangular coordinates and adding those components. Is that what you are doing?

My bad I will comment on my lines in the future as for what I am doing I wanted to sum the two vectors, so I first needed to decompose both vectors into their component form. Then, I added these components together and then used the Pythagorean theorem to find the magnitude.

berkeman
randomphysicsguy123 said:

Your image does not seem to match your problem statement. Why have you labeled ##\theta_1## down from the y-axis? Both angles should be referenced to the positive x-axis to get the signs and magnitudes right. And you are correct that you need to add the x and y components of each vector in rectangular coordinates to figure out the overall sum vector...

berkeman said:
This image was the one provided.

Last edited by a moderator:
That's hard to believe. (And you seem to have a problem with the Quote/Reply feature of the PF, but no big deal).

First of all, that figure is not SAT quality, so somebody else drew it. And somebody else mislabeled it.

#### Attachments

• 1602637326501.png
8.2 KB · Views: 91
It is not from an SAT prep book, it is from a free online SAT Physics site that provides example questions. Thus this is the real question. I am simply asking if I did it right and if not what did I do wrong and how to correct it.

randomphysicsguy123 said:
It is not from an SAT prep book, it is from a free online SAT Physics site that provides example questions. Thus this is the real question. I am simply asking if I did it right and if not what did I do wrong and how to correct it.
Fair enough. Is that the image that they provided, or your initial attempt at drawing it? I'm not trying to give you a hard time, I just need to understand what parts to translate into LaTeX for you as and example and to verify your work.

Can you please post a link to the original problem so that there is no more ambiguity? Thank you.

## 1. How do I add two vectors given in polar coordinates?

To add two vectors given in polar coordinates, you must first convert them to Cartesian coordinates. Then, you can add the x and y components of each vector separately to find the resultant vector. Finally, convert the resultant vector back to polar coordinates if needed.

## 2. What is the formula for adding two vectors in polar coordinates?

The formula for adding two vectors in polar coordinates is: R = (r1*cos(theta1) + r2*cos(theta2), r1*sin(theta1) + r2*sin(theta2)), where R is the resultant vector, r1 and r2 are the magnitudes of the two vectors, and theta1 and theta2 are the angles of the two vectors.

## 3. Can I add more than two vectors in polar coordinates?

Yes, you can add more than two vectors in polar coordinates by first converting them to Cartesian coordinates and then using the same process as adding two vectors.

## 4. How do I determine the direction of the resultant vector when adding two vectors in polar coordinates?

The direction of the resultant vector can be determined by finding the angle theta using the formula tan(theta) = (y-component)/(x-component). The angle theta represents the direction of the resultant vector from the positive x-axis.

## 5. Is there a graphical method for adding two vectors in polar coordinates?

Yes, you can use the graphical method of vector addition to add two vectors in polar coordinates. Draw the two vectors on a polar coordinate plane and use the parallelogram method to find the resultant vector. Then, convert the resultant vector back to polar coordinates if needed.

• Introductory Physics Homework Help
Replies
13
Views
597
• Introductory Physics Homework Help
Replies
2
Views
178
• Introductory Physics Homework Help
Replies
8
Views
335
• Introductory Physics Homework Help
Replies
2
Views
448
• Introductory Physics Homework Help
Replies
10
Views
341
• Introductory Physics Homework Help
Replies
1
Views
404
• Introductory Physics Homework Help
Replies
14
Views
398
• Introductory Physics Homework Help
Replies
8
Views
12K
• Introductory Physics Homework Help
Replies
4
Views
740
• Introductory Physics Homework Help
Replies
3
Views
190