# A car is driven 215 km west and then 85 km southwest. What is the displacement of the car from the point of origin (magnitude and direction)?

Mar 13, 2016

$\text{displacement="281,59 km" (magnitude)}$
$\theta = 77 , {68}^{o} \text{ from S to SW (angle of direction)}$

#### Explanation:

$x = 215 + 85 \frac{\sqrt{2}}{2} = 275 , 10 k m$
$y = 85 \frac{\sqrt{2}}{2} = 60 , 10$
$\text{displacement=} \sqrt{{\left(275 , 10\right)}^{2} + {\left(60 , 10\right)}^{2}}$
$\text{displacement="281,59 km" (magnitude)}$
$\tan \theta = \frac{275 , 10}{60 , 10} = 4 , 577$
$\theta = 77 , {68}^{o} \text{ from S to SW (angle of direction)}$