Question

ali walks 120m east 150m south 40m east find the distance and displacement

Answer 1

The distance

$$d=d_1+d_2+d_3=120+150+40=310\:\rm m$$

The displacement

$${\bf s}={\bf d}_1+{\bf d}_2+{\bf d}_3$$

where

$${\bf d}_1=120{\bf i}+0{\bf j},\; {\bf d}_2=0{\bf i}-150{\bf j}, \; {\bf d}_3=40{\bf i}+0{\bf j}$$

Hence

$${\bf s}=120{\bf i}+0{\bf j}+0{\bf i}-150{\bf j}+40{\bf i}+0{\bf j}=160{\bf i}-150{\bf j}$$

The magnitude of a displacement

$$s=\sqrt{(160)^2+(-150)^2}=219\:\rm m$$