Freddie Fisicks walks 215m,south and then goes 179 m, west. What is his resultant displacement? (magnitude and direction, of course)

Question

Freddie Fisicks walks 215m,south and then goes 179 m, west. What is his resultant displacement? (magnitude and direction, of course)

Answer 1

using XY coordinates, X is east, and Y is north, so south is -Y and west is -X.

215 m south is a vector of (0,-215) and 179 west is (-179,0), the resultant position is

(0,-215) + (-179,0) = (-129, -215), the magnitude is sqrt(179^2 + 215^2) = 279.76, and the angle

is arctan [(-215)/(-179)] in the third quadrant, which 50.22+180 = 230.22 deg.