Question:
A man has to go $50 \mathrm{~m}$ due north, $40 \mathrm{~m}$ due east and $20 \mathrm{~m}$ 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 $=50+40+20$ $=110 \mathrm{~m}$
$=110 \mathrm{~m}$
(b) Displacement $=50 \hat{\jmath}+40 \hat{\imath}-20 \hat{\jmath}$
$=40 \hat{\imath}+30 \hat{\jmath}$
$|\operatorname{disp}|=\sqrt{(40)^{2}+(30)^{2}}$
$=50 \mathrm{~m}$ at an angle of $\Theta=\tan ^{-1}\left(\frac{38}{40}\right)=37^{\circ}$ north to east
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