Vector Addition: Finding the Resultant Vector and Angle

[bwilhelm]

This one is giving me a headache.
Pretty sure i am wrong somewhere.
Did I add the vectors right?

Homework Statement

Vector A is 100 units at 30 degrees.
Vector B is 200 units at 140 degrees.
Find the vector sum R: R=A=B

Homework Equations

The Attempt at a Solution

So this is where I am:
100cos30 =86.6
100sin30 = 50

200cos140= -153
200sin140= 128.55

Add the X and Y's
86.6 -153= -67
50+128.55 = 178.55

Using Pyth. Thereom -67^2+ 178.55^2 = 165.5
so R= 155.5 units

Angle=
Tan (178.55/-67) then take the inverse Tangent = 75 degrees

 

[learningphysics]

You made a mistake with the pythagorean theorem. You should be squaring the entire component... ie: it should be:

(-67)^2 + 178.55^2

Not -(67^2) + 178.55^2

And the inverse tan is wrong.

 

[bengaltiger14]

Why is the inverse tan wrong?

 

[cosmic_tears]

Why is the inverse tan wrong?

You didn't take into account the sign. tan(75) > 0, whereas you got something negetive.

 

[learningphysics]

Yes, and arctan(178.55/67) = 69.43 not 75...

You need to use the fact that the angle is in the second quadrant, to get the exact angle... so it's 180-69.43 = 110.57.

 

[P.O.L.A.R]

Yes, and even if you ignore the sign, it comes to 69.4 not 75...

first and foremost you can't ignore the sign because negative arctan is in the 4th quadrent and the positive of that is in the 2nd quadrent. Ignoring the negative is something you cannot do.

 

[learningphysics]

first and foremost you can't ignore the sign because negative arctan is in the 4th quadrent and the positive of that is in the 2nd quadrent. Ignoring the negative is something you cannot do.

Yes, I know. I'm just pointing out that there's another mistake on top of the sign mistake.

 

[learningphysics]

first and foremost you can't ignore the sign because negative arctan is in the 4th quadrent and the positive of that is in the 2nd quadrent. Ignoring the negative is something you cannot do.

Don't you mean positive tan is the 1st and 3rd quadrant... negative tan is the 2nd and 4th quadrant?

 

[P.O.L.A.R]

Yes, I know. I'm just pointing out that there's another mistake on top of the sign mistake.

What mistake are you pointing out because you said to ignore the sign and you don't get the get the answer. If it is -75 you have to add 180 to get the angle in the right position which is 105 definitely different than 75. IS the answer negative or positive??

one more thing is that r=a=b or r=a+b?

 

[P.O.L.A.R]

Don't you mean positive tan is the 1st and 3rd quadrant... negative tan is the 2nd and 4th quadrant?

Yes but when you enter arctan in a calculator it gives you the answer in either the first or 4th quadrent.

 

[learningphysics]

What mistake are you pointing out because you said to ignore the sign and you don't get the get the answer. If it is -75 you have to add 180 to get the angle in the right position which is 105 definitely different than 75. IS the answer negative or positive??

one more thing is that r=a=b or r=a+b?

I was not telling him to ignore the sign. I said even if you ignore the sign...

Because arctan(178.55/-67) is not -75. It is -69.43. That is the mistake I was referring to.

So then the angle is 180-69.43 = 110.57.

 

[P.O.L.A.R]

I was not telling him to ignore the sign. I said even if you ignore the sign...

Because arctan(178.55/-67) is not -75. It is -69.43. That is the mistake I was referring to.

So then the angle is 180-69.43 = 110.57.

Ok I got you it just seemed that way.

I got the same thing by the way.

 

[learningphysics]

Ok I got you it just seemed that way.

I got the same thing by the way.

Yeah, I'm sorry. Poor choice of words... I'll edit the earlier post so he doesn't get confused.

 

[bwilhelm]

Thank you all very much!