Answer to Question #244552 in Physics for Asmar

Question

While exploring a cave, a spelunker starts at the entrance and moves the following distances. She

goes 75.0 m north, 250 m east, 125 m at an angle 30.0° north of east, and 150 m south. Find the resultant displacement

from the cave entrance.

Answer 1

Find the resultant displacement.

$A_N=75\text{ m},\\ A_E=0,\\ B_N=0,\\ B_E=250\text{ m},\\ C_N=125\sin30°,\\ C_E=125\cos30°,\\ D_N=-150 \text{ m}.\\ D_E=0.\\\space\\ R_N=A_N+B_N+C_N+D_N=-12.5\text{ m},\\ R_E=A_E+B_E+C_E+D_E=358\text{ m}.\\ R=\sqrt{R_N^2+R_E^2}=358\text{ m}.\\\space\\ \theta=\arctan\frac{|R_N|}{R_E}=2°\text{ S of E}.$