# Physics, Vectors?

##
In the sum A+B+=C, vector A has a magnitude of 11.4 m and is angled 48.4 degrees counterclockwise from the +x direction, and vector C has a magnitude of 14.8 m and is angled 16.6 degrees counterclockwise from the -x-direction. What are the A) magnitude and B) the angle (relative to +x) of B? state your angle as a positive number. I know it is A-C=B but I have the wrong answer please help and explain if you can. my incorrect answers are 8m and 33 degrees

In the sum A+B+=C, vector A has a magnitude of 11.4 m and is angled 48.4 degrees counterclockwise from the +x direction, and vector C has a magnitude of 14.8 m and is angled 16.6 degrees counterclockwise from the -x-direction. What are the A) magnitude and B) the angle (relative to +x) of B? state your angle as a positive number. I know it is A-C=B but I have the wrong answer please help and explain if you can. my incorrect answers are 8m and 33 degrees

##### 1 Answer

See discussion below.

#### Explanation:

A drawing is a major help. Are you familiar with the crude graphical ways to find a resultant vector? With this problem, I suggest using the method where you draw the first vector and then draw the second starting from the arrowhead of the first. Then the resultant is drawn from the beginning (tailfeathers) of the first to the end (arrowhead) of the second. If necessary, go to

http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html

and scroll down to the box immediately below the flow diagram a the top of this web page. The boxes below that might be useful later too.

We do not have the second vector details, that is what you are asked to find. But we can determine how to draw the second vector knowing the first and the resultant using this graphical method.

Draw the x axis with the origin. Using the given magnitude and angle, draw vector A, starting from the origin. Next draw the resultant, C, again starting from the origin. Now vector B will start at the arrowhead of A, and its arrowhead will be at the arrowhead of C. Draw that in and it will look like a completed graphical determination of the resultant of adding A and B.

So now you have a triangle and you know the length of 2 of its sides and you can calculate one of the angles from what you were given. B is the third of its sides. You could use the Law of Cosines to solve it or use the methods discussed on that hyperphysics page, but you can do it!

I hope this helps,

Steve