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 2 years ago
Determine the resultant of this vector sum: 10 N at 045 degrees, and 8 N at 68 degrees
 2 years ago
Determine the resultant of this vector sum: 10 N at 045 degrees, and 8 N at 68 degrees

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theEric
 2 years ago
Best ResponseYou've already chosen the best response.1This isn't so bad. Have you had practice with these?

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.1I can't do it with degrees :S

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1After a while, they'll become nearly routine!

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.1Can you please go through the steps , i find these really confusing

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1Okay! So you've seen these? And have learned that any vector has separate components (x and y)?

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1We can draw a picture, if you like. Let's look at the first vector, 10N. Sound good?

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1Alright! dw:1360640234142:dw There's the vector in one piece.

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.1How do we know that it's NE ?

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1That is the trick with degrees, and all you have to remember is this  and it'll be in the next picture. You're working with two dimensional space, here. A great way to draw this is the x and y axes that I bet you're familiar with. Everything has an x and y component, like the vectors. And people like to use angles! So they decided on a common place to start the angle, and where to go from there. I'll show you.

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.1OH so that's the common starting point ?

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1That's the convention. Convention just means it's a proper way to do it in some organization of math rules. So pretty much everybody does this. You could make up your own convention, but it'd be hard to explain it to the rest of us :P

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1Yep! Angle measures start from there if no other information is given!

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1360640896289:dwNow, a person might say, "10 degrees west of north" or something silly like that. That means....

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1But as a starting point, positive xaxis is what you'll use. Hopefully your teacher agrees. It's a farreaching convention.. Goes into lots of maths.

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1Now you know where your vector is! And you can split it up with trigonometric functions using the angle!

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1So you have seen that before? Using the trig functions?

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1@burhan101 so you've got it? Congrats and take care if you did!

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.1i know how to do these with like normal vectors

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1360641728957:dw

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.1i know thats not right .

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1You mean like <x,y>? Yeah, this is different. You aren't just told the components. However, you can find them!

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1Have you ever used sine or cosine for angles?

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1Well that's what you'll be doing here. Are you well practiced with them? Going back to this picture, dw:1360642770812:dwDo you see how to get the x and y components?

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1If not, I can show you.

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.1how do i add the other vector to this picture now

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1Well, vectors are easy to split up into components with sine and cosine. Then you use "vector addition," which really means you just add all like components! Then you have one vector as a result. And it is called the "resultant vector." And it'll be in <x, y> form. You can, however, get it back to how it was, with a given magnitude and given direction (as an angle).

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1Are you giving it a shot?

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.1Yes im trying to draw it out :$

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1I didn't see the picture you drew before! That's a good rough representation of the vectors! :) Just like mine! :)

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1360643739640:dw funy thing with vectors is that they are a magnitude (like 10N) and direction (like 45 degrees). They aren't a location. You can the same arrowed line anywheres, and they're still equal vectors.

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1The first drawing of the components is common, where the vectors start at the origin. But looking at it this next way will help see sine and cosine's roles.dw:1360644139377:dw

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1Actually, nevermind! Retake!

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1360644367333:dwThat one.

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1360644483191:dwand that one.

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1Do you see where this is going?

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.1Not realll dont i add the other 8 N at 068 degrees ?

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1Well, yeah! You have to add its components to the other vectors components. So, first, you have to get each vector's components.

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.1Dont you just add then like the tail to tail method and then do tan inverse to find the angle ? :S

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1You could, huh! But that's sort of what this is. Picture time! :)

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.1okay so im not totally off track

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1360645168898:dwderfinately not!

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1That last one shows the resultant vector.

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.1makes so much sense !

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.1so now i find the tan inverse right

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1After you get the components of the resultant vector, you use them to find the magnitude (however many N) and that inverse tangent (ycomponent divided by xcomponent) to find the angle.

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1Okay.... Ready to try it?

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1Not quite! Inverse tangent will give you an angle, but you have to give it a y/x amount. Since you want to find the angle of the really big resultant vector, you'll use its ycomponent divided by its xcomponent. You'll have those components after you do the adding. Let's break your 10N vector into components for practice. We can even then use those components to refind the angle!

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1\[\begin{matrix}xcomponent&=&10cos(45)&=&7.07\\ycomponent&=&10sin(45)&=&7.07\end{matrix}\]

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1And units are N. I'm gonna head to bed. Good luck! If you want to continue on your own, do the same thing to the 8N vector! Then, add the xcomponents together. Then add the ycomponents together. Then you have the resultant vectors components. That would be how you knew vectors before.

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.1thanks for your help ! :D

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1And to rediscover that magnitude and angle of the 10N vector, using it's x and ycomponents, Magnitude: Use Pythagorean Theorem.\[\sqrt{x^2+y^2}\] For the angle: Use inverse tangent.\[tan^{1}{\LARGE (}\frac{y}{x}\LARGE )\]

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1\[\sqrt{7.07^2+7.07^2}\approx 9.998\approx 10.00\]There was some rounding error to get to 9.998. But if you round it to the nearest hundredth, you have 10! \[tan^{1}{\LARGE (}\frac{7.07}{7.07}{\LARGE )}=tan^{1}(1)=45^o\]

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1Switched back. :) You're very welcome! Take care! Tag me if you need any more help.
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