Question

sally travels 50m west 120m south find the distance and displacement?

Answer 1

The distance

$$d=d_1+d_2=50+120=170\:\rm m$$

The displacement

$${\bf s}={\bf d}_1+{\bf d}_2$$

where

$${\bf d}_1=-50{\bf i}+0{\bf j},\; {\bf d}_2=0{\bf i}-120{\bf j}$$

Hence

$${\bf s}=-50{\bf i}+0{\bf j}+0{\bf i}-120{\bf j}=-50{\bf i}-120{\bf j}$$

The magnitude of a displacement

$$s=\sqrt{(-50)^2+(-120)^2}=130\:\rm m$$