# Objects A and B are at the origin. If object A moves to (4 ,-2 ) and object B moves to (5 ,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.

Sep 26, 2016

Velocity: $0.7603$ m/sec at ${80.54}^{\circ}$ (measuring counter clockwise from the X-axis)

#### Explanation:

Note that it doesn't matter that $A$ and $B$ started at the origin; it only matters that they started at the same place.

The initial distance between $A$ and $B$ is $0$ (meters)
The distance between $A$ and $B$ after $8$ seconds is
$\textcolor{w h i t e}{\text{XXX}} \sqrt{{\left(5 - 4\right)}^{2} + {\left(4 - \left(- 2\right)\right)}^{2}} = \sqrt{37}$ (meters)

Since this is the change in position relative to each other
the relative speed of $B$ from $A$'s perspective is
color(white)("XXX")(sqrt(37) "meters")/(8 "seconds") ~~0.7603453 "m/sec"

The tan of the angle (relative to the horizontal/X-axis) is $\frac{6}{1}$ (see diagram below).

Therefore the angular component of the velocity is
color(white)("XXX")"arctan"(6) ~~80.53768^@ 