Help with finding Resultant vectors using trig? I kind of know what I'm doing but I want verification I'm doing it correctly.

- BloomLocke367

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- chestercat

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- Jaynator495

*whistles while waiting*

- Jaynator495

annnyyyy day now...

- Jaynator495

and im waiting and im waiting and im waitng...

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## More answers

- Jaynator495

TYPE FASTER!!!! xD

- BloomLocke367

\(F_1=6.7~N~@ ~54°~W~of~N\)
\(F_2=9.2~N~@ ~26°~W~of~S\)

- Jaynator495

Jeese i go to help in math for the first time in a long time and people take forever to post the question! xD

- BloomLocke367

sorry XD I had to look up the code for the degree sign

- Jaynator495

XD

- BloomLocke367

I'm pretty sure I have to add \(90°\) to the first one because it's in the 3rd quadrant and you always start in the first for these problems (this is technically physics but it's still math lol)

- Jaynator495

you help them peachpi lel

- Jaynator495

*laughs away*

- BloomLocke367

I know I have to separate it in components and I do that using trig.. so.. hang on.. this will take some time for me to type out lol. please be patient.

- IrishBoy123

draw it :p
quicker/easier

- BloomLocke367

I can't.. my cursor goes BEHIND google chrome.. so I have to type it. /sigh

- Jaynator495

um, out of curiosity, is it a piticulair site orrr...

- BloomLocke367

IT'S GOOGLE CHROME. ONLY GOOGLE CHROME DOES IT. ALL SITES.

- BloomLocke367

sorry

- Jaynator495

LMAO

- BloomLocke367

anyhoo.. let me do math cx

- Jaynator495

i still dont know what to tell you... *laughs !!half!! to !^death^!*

- BloomLocke367

\(F_{1x}=6.7Cos(144)\\F_{1y}=6.7Sin(144)\\
F_{2x}=2.9Cos(244)\\F_{2y}=2.9Sin(244)\)
I know I then have to add \(F_{1x}\) and \(F_{2x}\) and add \(F_{1y}\) and \(F_{2y}\).

- BloomLocke367

@IrishBoy123

- BloomLocke367

is that correct so far?

- BloomLocke367

@phi

- phi

yes, that looks good

- BloomLocke367

okay so when I added \(F_{1x}\) and \(F_{2x}\) I got -1.48... but I have a calculator on my phone and I don't know if it's in radians or degrees so I'm not sure that's right...

- phi

up top you said F2 is 9.2
and in your calculations you are using 2.9
which is it ?

- BloomLocke367

dang it.. it's 9.2.. I accidentally wrote 2.9 :/ okay let me redo them.

- BloomLocke367

-9.45?

- phi

yes, for the x value

- BloomLocke367

okay now for y...

- BloomLocke367

-4.33?

- phi

yes

- BloomLocke367

so then I take \(F=\sqrt{(-9.45)^2+(-4.33)^2}\) right?

- phi

if you want the magnitude, yes

- BloomLocke367

yes that is what we are looking for at this moment. I'll find the degree next using tangent.

- BloomLocke367

I got 10.39. is that right?

- BloomLocke367

and I got 8.01° for the angle measure.. but both x and y are negative.. so it needs to be in the 3rd quadrant and is currently in the first.. so I have to add 180, correct? to get 188.01°

- BloomLocke367

wait.. that doesn't matter because they gave direction.. so instead I would just say 8.01° N of E, right?

- BloomLocke367

I don't know. .this is where I get confused.

- phi

you probably want to use 3 decimals in the calculation if you want 2 digit accuracy
I get mag 10.4 (rounded 10.3979)
No I did not get 8 degrees
type into google
atan(4.331/9.453) in degrees =

- BloomLocke367

wait.. why did you use those numbers? I used -4.33 and -9.45..

- phi

|dw:1443212499462:dw|

- BloomLocke367

wait nevermind *facepalm*

- phi

I used 3 digits (you can always round down later)
I ignored the 2 minus signs because they cancel each other

- BloomLocke367

I SEE WHAT I DID. I typed 1.33 and not 4.33 XD

- BloomLocke367

24.62?

- phi

yes, and that will be 24.6 degrees south of west or 65.4 degrees west of south

- BloomLocke367

wait.. why is it south of west?..

- phi

|dw:1443212895471:dw|

- BloomLocke367

I thought what we calculated was 24.6° N of E... and we would have to figure out S of W.. but I don't know.

- BloomLocke367

Is it because I added what I needed to in the beginning? so I don't have to at the end?

- phi

you changed 54º W of N to 144º (measured as we do in math, counter clockwise from the positive x-axis). similarly you changed 26º W of S to 244º
now add the vectors (head to tail)
|dw:1443213168068:dw|

- phi

you found the components of the dark vector <9, -4>
it is pointing south of west.
if we find the angle it makes with the (negative) x-axis we get 24.6º

- BloomLocke367

ohhh okay. I think I understand a little bit better. My main issue is figuring out what direction/angle the resultant vector is going.

- phi

using formulas (as you did) and drawing the vectors are very different ways of solving the problem. If you do it both ways, it is a good way to check your results.
the picture gives you a rough idea of the answer and the formulas give the exact numbers.

- BloomLocke367

Alright. The next one has 3 vectors.. I generally understand these they just take me a very long time to do them. :/

- BloomLocke367

Do you mind if I open a new question and tag you?

- phi

yes, a new post is better

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