A student walks 350 m [S], then 400 m [E20°N], and finally 550 m [N10°W]. Using the component method, find the resultant (total) displacemen

Question

A student walks 350 m [S], then 400 m [E20°N], and finally 550 m [N10°W]. Using the component method, find the resultant (total) displacement). Round your answer to the appropriate significant figures. Round your angle to the nearest degree.

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MichaelMet 4 years 2021-07-13T12:38:10+00:00 1 Answers 1 views 0

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  1. thuthao
    0
    2021-07-13T12:39:37+00:00
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    In component form, the displacement vectors become

    • 350 m [S]   ==>   (0, -350) m

    • 400 m [E 20° N]   ==>   (400 cos(20°), 400 sin(20°)) m

    (which I interpret to mean 20° north of east]

    • 550 m [N 10° W]   ==>   (550 cos(100°), 550 sin(100°)) m

    Then the student’s total displacement is the sum of these:

    (0 + 400 cos(20°) + 550 cos(100°), -350 + 400 sin(20°) + 550 sin(100°)) m

    ≈ (280.371, 328.452) m

    which leaves the student a distance of about 431.8 m from their starting point in a direction of around arctan(328.452/280.371) ≈ 50° from the horizontal, i.e. approximately 431.8 m [E 50° N].

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