# Objects A and B are at the origin. If object A moves to (3 ,1 ) and object B moves to (2 ,4 ) over 8 s, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.

Jul 8, 2016

(Using the positive Y-axis as North)
$1.118 \frac{m}{s} \text{ at } {47.16}^{\circ} W o f N$

#### Explanation:

Distance after $8 s$ between A and B
$\textcolor{w h i t e}{\text{XXX}} d = \sqrt{{\left(3 - 2\right)}^{2} + {\left(1 - 4\right)}^{2}} = \sqrt{10}$ (m)
Speed of B relative to A: $\frac{\sqrt{10}}{8} \frac{m}{s} \approx 1.118 \frac{m}{s}$

If $\theta$ is the angle from A to B (relative to the Y-axis)
then $\tan \left(\theta\right) = \frac{4 - 1}{2 - 3} = - 3$
$\Rightarrow \theta \approx {137.16}^{\circ}$ (relative to the positive X-axis)
or
$\textcolor{w h i t e}{\text{XXX}} {47.16}^{\circ}$ (relative to the Y-axis)