# A delivery truck travels 18 blocks north, 10 blocks east, and then 20 blocks south. What is the truck's final displacement form it's starting point? Assume the blocks are all equal length.

Aug 31, 2017

$\vec{s} = 10 \hat{i} - 2 \hat{j} \text{ units}$
$| \vec{s} | \approx 10.1 \text{ units}$

#### Explanation:

Let us consider the starting point of the truck as origin

Let $\vec{s}$ be the displacement vector of truck from origin

$\therefore$ According to the question,

$\vec{s} = 18 \hat{j} + 10 \hat{i} - 20 \hat{j} \text{ units}$

$\Rightarrow \vec{s} = 10 \hat{i} - 2 \hat{j} \text{ units}$

Magnitude of displacement $| \vec{s} | = \sqrt{\left({10}^{2}\right) + {\left(- 2\right)}^{2}}$

$= \sqrt{102}$

$\approx 10.1 \text{ units}$