# Objects A and B are at the origin. If object A moves to (3 ,-2 ) and object B moves to (2 ,9 ) over 5 s, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.

Oct 10, 2016

Relative velocity of $B$ with respect to $A$ is $2.21 \text{ m/s}$ at an angle of ${95.2}^{\circ}$ (relative to the positve X-axis)

#### Explanation:

After moving $A$ to $\left(3 , - 2\right)$ and $B$ to $\left(2 , 9\right)$
from $A$'s perspective $B$ has moved $< - 1 , 11 >$
for a distance of $\sqrt{{\left(- 1\right)}^{2} + {11}^{2}} = \sqrt{122}$
Since this apparent motion takes place over $5$ seconds
the apparent speed is $\frac{\sqrt{122}}{5} \text{ m/s"~~2.21 " m/s}$

The angle of this apparent motion, $\theta$ (relative to the positive X-axis) is such that $\tan \left(\theta\right) = \frac{11}{- 1}$

"arctan(-11/1) ~~1.66 (radians) $\approx {95.2}^{\circ}$