Question

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

Answer 1

$\overrightarrow{AD}=2\hat{i}+0.5\hat{j}+4\hat{i}$

= $6\hat{i}+0.5\hat{j}$

$AD=\sqrt{A{E}^2+D{E}^2}$

=$\sqrt{6^2+(0.5{)}^2}$

=6.02 km

Now, tan $\theta =\frac{DE}{AE}=\frac{.5}{6}$

$\Rightarrow \theta =ta{n}^{-1}\left(\frac{1}{12}\right)$

Hence displacement of the car is 6.02 km along the direction $ta{n}^{-1}\left(\frac{1}{12}\right)$ with +ve
x-axis.