A body travels a distance of $3\ km$ towards East, then $4\ km$ towards North and finally $9\ km$ towards East.
(i) What is the total distance travelled ?
(ii) What is the resultant displacement ?

The motion of the boy has been shown in the below figure:

(i). Total distance traveled by the boy $=3\ km+4\ km+9\ km=16\ km$

(ii). In the above diagram, the journey of the boy has been represented.

AC  is the displacement.

And to find the value of the displacement $(AC)$ let us use Pythagoras theorem in $\vartriangle ABC$

$AC^2=AB^2+BC^2$

Or $AC^2=(9+3)^2+4^2$

Or $AC^2=12^2+4^2$

Or $AC^2=144+16$

Or $AC^2=160$

Or $AC=\sqrt{160}$

Or $AC=12.5\ km$

Therefore, the displacement is $12.5\ km$.

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Updated on: 10-Oct-2022

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