# Resultant displacement and angle

1. Aug 29, 2006

### bearhug

While exploring a cave, a spelunker starts at the entrance and moves the following distances. She goes 69.7 m north, 246.8 m east,127.4 m at an angle 37.8 (degrees) north of east, and 127.4 m south. What is the resultant displacement from the cave enterance? The angle should be positive between 0 and 360.

I drew a diagram not 100% accurate but enough to give me a picture. And the resultant displacement I took to be the distance from point A to point D (start point to end point). The equations I used are as follows:
ax= 69.7 cos(90) ay= 69.7 sin(90) = 0, 69.7
bx= 246.8 cos (0) by= 246.8 sin (0) = 246.8, 0
cx= 127.4 cos(37.8) cy= 127.4 sin(37.8) = 100.7, 78.1
dx= 127.4 cos(90) dy= 127.4 sin(90) = 0, 127.4

I found Rx = 347.5
Ry = 275.2

R = (347.5^2 + 275.2^2)^1/2
= 443.2m to be the resultant displacement

angle = tan= 275.2/347.5= 38.4 degrees

Is this the right method?

2. Aug 29, 2006

### Staff: Mentor

Rewrite that last equation. If "north" is at an angle of 90 degrees, then south must be directly opposite, which is 270 degrees (or -90 degrees).

(Other than that error, your method looks just fine.)

Last edited: Aug 29, 2006
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook