# Objects A and B are at the origin. If object A moves to (5 ,-1 ) and object B moves to (-8 ,1 ) over 3 s, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.

Apr 26, 2016

Treating the positive X-axis as North,
color(white)("XXX")"approximately "4.38 m/(sec)" at "8.75^@ N" of "W

#### Explanation:

The distance between points A and B has increased from $0$ meters to
$\textcolor{w h i t e}{\text{XXX}} \sqrt{{\left(5 - \left(- 8\right)\right)}^{2} + {\left(1 - \left(- 1\right)\right)}^{2}} = \sqrt{173} \approx 13.15$ meters
for an average speed of
$\textcolor{w h i t e}{\text{XXX}} \frac{\sqrt{173} m}{3 \sec} \approx 4.38 \frac{m}{\sec}$

Relative to A, B has moved $13$ meters East and $2$ meters North.
If $\theta$ is the angle North of due East for B's movement relative to A then
$\textcolor{w h i t e}{\text{XXX}} \tan \left(\theta\right) = \frac{2}{13}$

$\textcolor{w h i t e}{\text{XXX}} \Rightarrow \theta = \arctan \left(\frac{2}{13}\right) \approx {8.75}^{\circ}$

(Remember that velocity must always include a direction as well as a speed).