Question:
A man has to go 50m due north, 40m due east and 20m due south to reach a field.
(a) What distance he has to walk to reach the field?
(b) What is his displacement from his house to the field?
Solution:
(a) Distance travelled = 50+40+20 =110m
(b) Displacement = 50 ĵ +40 î- 20ĵ
= 40î+30 ĵ
$|\operatorname{disp}|=\sqrt{(40)^{2}+(30)^{2}}$
$=50 \mathrm{~m}$ at an angle of $\Theta=\tan ^{-1}\left(\frac{30}{40}\right)=37^{\circ}$ north to east