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

The displacement of the car is represented by $\overrightarrow{\mathrm{AD}}$.
$$\begin{gathered} \overrightarrow{\mathrm{AD}}=2\hat{i}+0.5\hat{j}+4\hat{i} \\ =6\hat{i}+0.5\hat{j} \end{gathered}$$

Magnitude of $\overrightarrow{\mathrm{AD}}$ is given by

$$\begin{gathered} \mathrm{AD}=\sqrt{{\mathrm{AE}}^2+{\mathrm{DE}}^2} \\ =\sqrt{6^2+{\left(0.5\right)}^2} \\ =\sqrt{36+0.25}=6.02\mathrm{km} \end{gathered}$$



Now, $\tan \mathrm{\theta }=\frac{\mathrm{DE}}{\mathrm{AE}}=\frac{1}{12}$
$\Rightarrow \mathrm{\theta }={\tan }^{-1}\left(\frac{1}{12}\right)$
Hence, the displacement of the car is 6.02 km along the direction ${\tan }^{-1}\left(\frac{1}{12}\right)$ with positive the x-axis.