Vectors and Motion in Two Dimensions

AP Physics 1· difficulty 2/5

A hiker walks 9 km9~\text{km} east, then 12 km12~\text{km} north. What is the magnitude of his net displacement?

  • A

    21 km21~\text{km}

  • B

    108 km108~\text{km}

  • C

    15 km15~\text{km}

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  • D

    3 km3~\text{km}

Explanation

By the Pythagorean theorem, Δr=92+122=225=15 km|\Delta\vec r| = \sqrt{9^2 + 12^2} = \sqrt{225} = 15~\text{km}.

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