# Objects A and B are at the origin. If object A moves to (-8 ,-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.

Mar 4, 2016

Object B moves away from object A with a speed of $1.202$ $\frac{m}{\sec}$ in a direction given by $- {33.7}^{o}$ relative to $x$ axis.

#### Explanation:

As object A moves to $\left(- 8 , - 2\right)$ and object B moes to $\left(- 5 , - 4\right)$, the distance between them after $3$ seconds is

$\sqrt{{\left(- 5 - \left(- 8\right)\right)}^{2} + {\left(- 4 - \left(- 2\right)\right)}^{2}}$ i.e. $\sqrt{{3}^{2} + {\left(- 2\right)}^{2}}$ or

$\sqrt{9 + 4} = \sqrt{13} = 3.606$

Hence object B moves away from object A with a speed of $\frac{3.606}{3} = 1.202$ $\frac{m}{\sec}$.

Direction is given by ${\tan}^{-} 1 \left(\frac{- 4 - \left(- 2\right)}{- 5 - \left(- 8\right)}\right) = {\tan}^{-} 1 \left(- \frac{2}{3}\right) = - {33.7}^{o}$ relative to $x$ axis