While exploring a cave, a spelunker starts at the entrance and moves the following distances: 75.0 m north, 260 m east, 195 m at an angle 30.0° north of east, and 150 m south. Find the resultant displacement from the cave entrance.

Answer 1

Let x=east, y=north
and 0° towards the +x-axis (due East)
and 90° = due north.
Separate each displacement into the x- and y-components and add.
distance angle x y
75m N=90° 75cos(90°) 75sin(90°)
260m E=0° 260cos(0) 260sin(0)
195m 30°N of E = 30° 195cos(30°) 195sin(30°)
...

Add up algebraically the x- and y-components. The sum will be the x- and y-components of the resultant displacement vector.

Answer 2

A cave explorer is called a speleologist.

Answer 3

While exploring a cave, a spelunker starts at the entrance and moves the following distances. She goes 75.0 m north, 250 m east, 116 m at an angle 30.0° north of east, and 156 m south. Find the resultant displacement from the cave entrance. The figure below suggests the situation but is not drawn to scale.