How Do You Calculate Vector Sums and Differences Graphically?

[soul814]

umm i did that... i get a different answer from the book

(2.6,1.5)

the other one is three but the same thing can be done to found it
3cos(90),3sin(90)

(0,3)

 

[arildno]

(2.6,1.5) looks right;
what does your calculator say when you type in cos(30)?
Multiply that number with 3.

 

[soul814]

i get .8660254038

*3 = 2.598076211

How would you get the answer after that?

Rx = Ax + Bx = 2.6 + 0
Ry = Ay + By = 1.5 + 3

Now I add Rx + Ry = 7.1

Answer in book is 5.2m at 60 above x-axis

 

[arildno]

HAVE YOU FORGOTTEN PYTHAGORAS?

The resultant vector is:
(\frac{3\sqrt{3}}{2},\frac{9}{2})
The length is therefore:
\sqrt{\frac{27}{4}+\frac{81}{4}}=\frac{\sqrt{108}}{2}

 

[soul814]

how did u get the resultant vector?

 

[arildno]

\cos(30)=\frac{\sqrt{3}}{2},\sin(30)=\frac{1}{2}
(This is a rather well-known relation; you'll it later on)
Hence A has coordinates (\frac{3\sqrt{3}}{2},\frac{3}{2})
Summing A with B (coord. (0,3)) yields the resultant vector).

 

[soul814]

ahh indeed it does.. this makes sense now :D

yes I learned cos(30) = 3/2 in precalculus the 30-60-90 triangle

 

[soul814]

wohoo got B) correct how would you get the degree though?

 

[arildno]

How do you think?

 

[soul814]

ummm I know all the measurements of the sides yet no angles except that 30 degrees, but its on the outside

 

[arildno]

But you know its horizontal and vertical coordinates, right?
How can you calculate the tangent of the angle using that info?

 

[soul814]

the figure isn't a right triangle though

 

[arildno]

You are to find the resultant vectur's angle to the x-axis; how can you construct a triangle in such a manner that the coordinates you've been given will help you find that angle?

 

[soul814]

OOO I got it :D

extend the Line downward so the verticles of the triangle are

tan^-^1 = 4.5/2.6

(0,0) --> (2.6,0) --> (2.6,4.5)

 

[arildno]

You should get 60 degrees..

 

[soul814]

Yep I got 60 degrees 59.9 i think. Thanks for your help :D

nice i think i got section 3.2 and 3.3 of my textbook down ahah... tommo I will probably ask about projectile motion, hopefully you'll help me again. The textbook leaves out a lot of information. Like it leaves out little steps.

 

[arildno]

No problem..

 

[shweta tiwari]

its an emergency...i really need to know this...

can two vectors representing two different physical quantities be equal?

can force and displacement be equal vectors if they are in same direction and have same magnitude?? doesn't representing different phy. quantities makes them different vectors?

 

[Rayquesto]

I hate vectors! I'm in physics A and I don't get it, even though I understand all of the force, energy, and projectile motion stuff.