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Oracle
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posted by  Sea Salt on 10/5/2008 7:08:04 PM  |  status: Closed  

direction of vector

Course Textbook Chapter Problem
Calculus Based Physics Physics For Scientists And Engineers 7th by Jewett, Serway 3 15P
Question Details:
A vector has an x-component of -25.0 units and a y component of 40.0 units. Find the magnitude and direction of this vector.

*I found the magnitude to be 47.2 units but the direction part is confusing to me. I get -58.0 degrees and the book says it's 122 degrees and I don't quite understand why. Thank you in advance.


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Oracle
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posted by Ctrl on 10/5/2008 10:22:36 PM  |  status: Live
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Sea Salt's comment:
"thank you for your time and help"
Response Details:
I'm just speculating, but, there are a few things to note.

1)  somewhere it says to report all angles counter clockwise from the positive x axis
2)  need to look at where x and y are to determine whether the direction makes sense, so on this problem

the direction is given by:    

or   ------>   

Now, since x is negative, but y is positive, this angle must lie in the 3rd quadrant, and it cannot then be negative

So the angle measures approximately 57.9946 degrees from the negative x axis, that means that if you were to measure this angle from the positive x axis (as stated in (1)), you would add 90 degrees + 90-57.9946 = 122.005

or rounding this 122 degrees

hope this helps, and again, this is just me speculating, but it makes sense to me :-)

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