# Objects A and B are at the origin. If object A moves to (-6 ,-2 ) and object B moves to (-5 ,-4 ) 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.

Jul 7, 2016

${v}_{\text{AB"=sqrt5/3 " }} \frac{m}{s}$
$\text{please look over the animation}$

#### Explanation:

$\vec{a} : \text{represents velocity of B from perspective of A}$
$u : \text{(red vector) represents velocity of A}$
$v = u : \text{represents velocity of B}$

$\text{note that } \vec{a} = \vec{w} - \vec{u}$

$\text{you need to find the relative displacement}$
$\text{let "Delta x" be relative displacement}$
$\text{please look over the figure above}$

$\Delta x = \sqrt{A {G}^{2} + G {B}^{2}}$

$\text{or:}$

$A = \left(- 6 , - 2\right) \text{ ; } B = \left(- 5 , - 4\right)$
$\Delta x = \sqrt{{\left(- 5 + 6\right)}^{2} + {\left(- 4 + 2\right)}^{2}}$

$\Delta x = \sqrt{{1}^{2} + {\left(- 2\right)}^{2}} = \sqrt{1 + 4} = \sqrt{5}$

$\Delta t = 3 \text{ } s$

${v}_{\text{AB}} = \frac{\Delta x}{\Delta t}$

${v}_{\text{AB"=sqrt5/3 " }} \frac{m}{s}$