Question

A spy report about a suspected car reads as follows. "The car moved $2.00km$ towards east, made a perpendicular left turn, ran for $500m$, made a perpendicular right turn, ran for $4.00km$ and stopped". Find the displacement of the car.

Answer 1

Mention East by $i$

west by $-i$

North by $j$

and South by $-j$

Now coming to motion initially $2km$ towards east so $2i$

Then left turn means north and $0.5km$ so $0.5j$

Then a right turn means again $east$ and $4.0km$ so $4i$

net displacement will be $2i+0.5j+4i=6i+0.5j$

magnitude will be $\sqrt{6^2+{0.5}^2}=6.02km$