# Objects A and B are at the origin. If object A moves to (9 ,7 ) 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.

Nov 8, 2016

$\left(- \frac{17}{3} \text{m/s", -8/3 "m/s}\right)$

#### Explanation:

The velocity of A, ${V}_{\text{A}}$ is given by its displacement over the time taken.

V_"A" = 1/(3"s") * [((9"m"), (7"m")) - ((0"m"), (0"m"))] = ((3 "m/s"), (7/3 "m/s"))

Similarly, the velocity of B, ${V}_{\text{B}}$ is given by

V_"B" = 1/(3"s") * [((-8"m"), (-1"m")) - ((0"m"), (0"m"))] = ((-8/3 "m/s"), (-1/3 "m/s"))

In the frame of A, B looks as if it is traveling with velocity

V_{"B rel A"} = V_"B" - V_"A"

$= \left(\left(- \frac{8}{3} \text{m/s"), (-1/3 "m/s")) - ((3 "m/s"), (7/3 "m/s}\right)\right)$

$= \left(\begin{matrix}- \frac{17}{3} \text{m/s" \\ -8/3 "m/s}\end{matrix}\right)$