A spelunker is surveying a cave. She follows a passage 120 m straight west, then 210 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.

Question

A. Use a scale drawing to determine the magnitude of the fourth displacement.

B. Determine the direction of the fourth displacement. (....) south of west

Answer 1

Unless otherwise stated, all angles are measured CCW from the
+x-axis.

D = -120 + 210[315o] + 280[60o].

X = -120 + 210*Cos315 + 280*Cos60
= 168.5 m.
Y=210*sin315 + 280*sin60 = 94 m.

Tan A = Y/X = 94/168.5 = 0.55786
A = 29.2o

D = X/Cos A = 168.5/Cos29.2 = 193 m[29o].

b. Direction = 29 + 180 = 209o =
29o S. of W.