Answer :
Final answer:
The person's total displacement, after resolving each leg of the journey into its northward or southward and westward components and combining them, is approximately 72.0 m through the use of the Pythagorean theorem.
Explanation:
When a person walks 12.0° north of west for 55.0 m and 63.0° south of west for 25.0 m, we can resolve each leg of the journey into the westward and northward components. For the first leg, the components are 55.0 m * cos(12.0°) for westward and 55.0 m * sin(12.0°) for northward displacement. For the second leg, the components are 25.0 m * cos(63.0°) for westward and -25.0m * sin(63.0°) for southward displacement (the southward displacement is negative as we are considering north as positive).
Adding the westward components and the northward (and southward) components together and then applying the Pythagorean theorem results in the total displacement. In this case, it comes out to be approximately 72.0 m, which corresponds with option 'b'.
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