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A spelunker is surveying a cave. She follows a passage 180 m straight west, then 230 m in a direction 45° east of south, and then 280 m at 30° east of north. After a fourth unmeasured displacement, she finds herself back where she started. A: Use a scale drawing to determine the magnitude of the fourth displacement. Express your answer using two significant figures.
B: Determine the direction of the fourth displacement. Express your answer using two significant figures.

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Answer:

A) D = 146.34m

B) α = 33.07° south of west

Explanation:

In the diagram you can see the position after each displacement.

Point A will be at (-180,0) in rectangular coordinates

Point B will be at (-180,0) + (230*cos(45), -230*sin(45))=(-17.365, -162.635)

Point C will be at Pb + (280*sin(30), 280*cos(30)) = (122.635, 79.852)

The fourth displacement will therefore be: (-122.635, -79.852).

The module of this vector is 146.34m

And the angle is 33.07° south of west

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