Question

ahmer walks 100m east 70m north 140m east find the displacement and distance?

Answer 1

The distance

$$d=d_1+d_2+d_3=100+70+140=310\:\rm m$$

The displacement

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

where

$${\bf d}_1=100{\bf i}+0{\bf j},\; {\bf d}_2=0{\bf i}+70{\bf j}, \; {\bf d}_3=140{\bf i}+0{\bf j}$$

Hence

$${\bf s}=100{\bf i}+0{\bf j}+0{\bf i}+70{\bf j}+140{\bf i}+0{\bf j}=240{\bf i}+70{\bf j}$$

The magnitude of a displacement

$$s=\sqrt{(240)^2+(70)^2}=250\:\rm m$$