Disclaimer: This is not for any class. I have downloaded this book ( http://www.ck12.org/book/CK-12-Physics---Intermediate/ ) and am ( attempting to (: ) work through it on my own. I am going through the section on relative motion ( section 3.3 in the book ) and am confused by a portion. It goes: (copy/pasted from book)(adsbygoogle = window.adsbygoogle || []).push({});

Car A is moving due east with a speed of 30 mph and Car B is moving due north with a speed of 30 mph.

a. What is the velocity of car A relative to car B?

Vab =~Va - Vb The two vectors are not along the same line so we’ll use their components

Va = (+30;0) and Vb = (0;+30), where east is +x and north is +y

-Vb = (0;-30), therefore, Va - Vb = (30+0;0-30) = (+30;-30). The components are directed east and south, so

the direction is southeast. Since both components have the same magnitude, the angle must be 45. But since the

vector is in the southeast direction it is in the 4th quadrant so the angle is 315, and the magnitude is the Pythagorean

sum (30[^]2 +30[^]2) [^]1/2 = 42:4 mph.

What is most confusing is when they state, "Since both components have the same magnitude, the angle must be 45." I see that both cars (vectors?) have the same magnitude (30mph?), but how does that mean "the angle must be 45"? And then they state that because the vector has a southeastern direction it is in the 4th quadrant, so the angle is 315... Where does the angle of 315 come into play at all? I see them state the angle then not use it directly in any formula.

Can someone help shine some light on this matter for me? Thanks in advance!

EDIT: It seems I have posted in the wrong area. Sorry :)

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# Relative Motion

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