# Objects A and B are at the origin. If object A moves to (-5 ,-1 ) and object B moves to (5 ,3 ) 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.

Feb 25, 2016

Velocity is $3.59$ m/s in the direction given by $\theta = {21.8}^{o}$

#### Explanation:

The movement of $B$ relative to $A$ is given by ((5-(-5)),(3-(-1)) or $\left(10 , 4\right)$.

Converting $\left(10 , 4\right)$ to polar coordinates $\left(r , \theta\right)$, they are given by$r = \sqrt{{10}^{2} + {4}^{2}}$ and $\theta = {\tan}^{- 1} \left(\frac{4}{10}\right)$ i.e. $r = \sqrt{116}$ and $\theta = {\tan}^{- 1} 0.4$

i.e. $r = 10.77$ and $\theta = {21.8}^{o}$

As the distance is covered in $3$ seconds,

Velocity is $\frac{10.77}{3} = 3.59$ m/s in the direction given by $\theta = {21.8}^{o}$