Repeat the problem above, but reverse the order of the two legs of the walk; show that you get the same final result. That is, you first walk leg B\vec{B} , which is 20.0 m in a direction exactly 4040^\circ south of west, and then leg A\vec{A}, which is 12.0 m in a direction exactly 2020^\circ west of north. (This problem shows that A+B=B+A\vec{A} + \vec{B} = \vec{B} + \vec{A} .)
<b>Figure 3.56</b>
Figure 3.56
Question by OpenStax is licensed under CC BY 4.0
Final Answer
19.5 m, 4.66 S of W19.5 \textrm{ m, } 4.66^\circ \textrm{ S of W}

Solution video

OpenStax College Physics, Chapter 3, Problem 6 (Problems & Exercises)

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when finding Rx why is it not -12m for Ax? The arrow is pointing to the left.

Hi propiak,
Thank you very much for noticing this. You're quite right that AxA_x should be negative, and the same is true for BxB_x. It turns out to not affect the final answer since, when finding the magnitude of the resultant, we square the components of the resultant so the negative sign doesn't matter. Where is might have mattered is in finding the angle, but I ended up changing the sign of RyR_y from negative to a positive so that RyR_y divided by RxR_x was positive. This was justified by looking at the picture, and thinking only about the magnitudes of the components, then specifying direction at the end based on the picture. Looking at the drawing is what informed direction rather than using the signs to give direction. Admittedly, the signs were important for finding RyR_y since the y-components of AA and BB are in opposite directions and there needs to be subtraction to find RyR_y. I can see why this is confusing, and I'll flag this video for a re-do some day, but I hope with these comments that it makes enough sense in the mean time to help.
All the best,

This video was updated on Nov. 2nd, 2023