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4 October, 23:34

A hiker walks 50 miles 55 degrees south of west. How far did she walk west?

Select one:

a. 28.7 miles

b. 40.9 miles

c. 35.4 miles

d. none of the above

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Answers (1)
  1. 4 October, 23:55
    0
    She walked 28.7 miles west ⇒ answer a

    Explanation:

    A hiker walks 50 miles 55 degrees south of west

    That means the magnitude of her displacement is 50 miles

    55 degree south of west means the angle between her displacement

    direction and the west is 55°

    We need to find how far she walk west

    Her walk to west is the horizontal component of her displacement

    West is adjacent to the angle of direction

    If the magnitude of her displacement is R and its direction is Ф, then

    → The horizontal component = R cos Ф

    → R = 50 miles, Ф = 55°

    → The horizontal component = 50 cos (55) = 28.7 miles

    The horizontal component represents her walk to the west

    She walked 28.7 miles west
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