Physics: Adding Vectors?

I'm confused on how to find the direction of the resultant using the x and y components. So please help me.





Example: Add these vectors.


a) 150 m, 300 degrees


b) 75 m, 65 degrees


c) 195 m, 195 degrees





I found each of the x and y components and added them together and got: x= 212.1, y= 322.3


I drew out the right triangle and found the hypotnuse= 385.8


What do I do next? How do I find the direction?

Physics: Adding Vectors?
angle = tan^-1 322.3/212.1
Reply:OK you've done the hard part...finding all the x's and y's. And you've added them to get X = 212.1 and Y = 322.3.





Here's how you get the direction. Recognize that X and Y are just two side of a right triangle. We usally graph the X in the horizontal direction and the Y in the vertical. And you have the hypo S = 385.8 running from X to Y. And we have...


Y


|\


| .\


| .. \ S


|.... \


___oX What's that gap between S and X at o? It's an angle, and that's the direction of S relative to the X axis. Let's call that gap theta = arctan(Y/X) = arctan(322.3/212.1). And there you have it, do the math and you'll have an angle theta to go along with S = 385.8.





As you failed to give the basis for your angles (e.g., what's zero degrees?), I have no clue what direction those angles you gave are pointing. But using arctan(Y/X) is the way you find the direction, once you have established the zero point.
Reply:The angle @ between the resultant and X axis is:


tan@ = Y/X = 322.3/212.1


So , @ = 56°39'
Reply:Having the degrees, you could use this formula to find x-y coordinates of vectors:


x = 150*cos((300/180)*pi) ; y = 150*sin((300/180)*pi)


and so on for the other vectors


After that, you have to sum each components and finally find the degree as follows


let alpha vector degree relevant to x axis, then





alpha = arctan(y/x)





Amplitude or module (I don't know if you call it so) is


sqrt(x^2+y^2)