Question
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 $\vec{B}$ , which is 20.0 m in a direction exactly $40^\circ$ south of west, and then leg $\vec{A}$, which is 12.0 m in a direction exactly $20^\circ$ west of north. (This problem shows that $\vec{A} + \vec{B} = \vec{B} + \vec{A}$ .)
$19.5 \textrm{ m, } 4.66^\circ \textrm{ S of W}$

# OpenStax College Physics, Chapter 3, Problem 6 (Problems & Exercises)  In order to watch this solution you need to have a subscription.

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### Calculator Screenshots

• • Thank you very much for noticing this. You're quite right that $A_x$ should be negative, and the same is true for $B_x$. 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 $R_y$ from negative to a positive so that $R_y$ divided by $R_x$ 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 $R_y$ since the y-components of $A$ and $B$ are in opposite directions and there needs to be subtraction to find $R_y$. 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.