While exploring a cave, a spelunker starts at the entrance and moves the following distances: 75.0 m north, 225 m east, 160 m at an angle 30.0° north of east, and 150 m south. Find the resultant displacement from the cave entrance.

Answer 1

You have four vectors.
For each one resolve them into North and east components.
Adding the North components.
N= 75 + 0 + 125 sin(30) - 150 = - 12.5 m
And adding the east components we get
E = 0 + 250 + 125 cos(30) + 0 = 358.25

The magnitude of the result is found by Pythagoras' theory
C = sqrt (a^2 + b^2)
= 358 m to three significant figures.

And the angle is south of east.
found by arctan (12.5/358.25)
= 2 degrees south of East.