A spelunker is surveying a cave. He follows a passage that goes 179 m straight west,...

A spelunker is surveying a cave. He follows a passage that goes 179 m straight west, then 211 m in a direction 45° east of south, then 285 m at 30° east of north. After a fourth unmeasured displacement he finds himself back where he started. Use a scale drawing to determine the fourth displacement.

a) magnitude	_______ m
b) direction	_______° SELECT ONE -----> : (north of east) (south of east) (south of west) (north of west)

Expert Solution

vector X- component Y-component

179 m west - 179 0

211 m 45° east of south 211 Sin45 - 211 Cos45

285 m at 30° east of north 285 Sin30 285 Cos30

Net displacement in X-direction = -179 + 211 Sin45 + 285 Sin30 = 112.7 m

Net displacement in Y-direction = 0 - 211 Cos45 + 285 Cos30 = 97.6

so net fourth displacement = sqrt (112.7² + 97.6²) = 149.1 m

= tan^-1 (Y/X) = tan^-1(97.6/112.7) = 40.89 north of east

genius_generous answered 4 months ago

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