a) South: , West
b) SW: , NW:
Note: in part B Shaun mistakenly switched units to meters instead of kilometers. The numbers are all correct, but please think "km", when you see "m".
OpenStax College Physics, Chapter 3, Problem 21 (Problems & Exercises)
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why do you make the units for part B meters and not km
Hello kmonegro151, thank you for noticing that mistake! I've made a note of it for other students. The numbers are correct, but the units should be "km".
The explanation made no sense to me why do you rotate the coordinate system
Hi tresor, thank you for the question. Strictly speaking, we don't need to rotate the coordinate system. It was suggested in the question, and it's a convenient way to approach the problem since the two legs of the alternative route are perpendicular, just like the coordinate axes are, but there is a different way. Instead of rotating the coordinate system, you could draw the two vectors described in part (b), along with the resultant from the origin (of the original coordinate system) to the destination. These three arrows make a triangle, and then you could figure out the length of each leg after sorting out what the angles are by inspecting the picture.
Hope this helps,