# Objects A and B are at the origin. If object A moves to (2 ,1 ) and object B moves to (5 ,2 ) over 4 s, what is the relative velocity of object B from the perspective of object A?

Feb 9, 2017

$\frac{\sqrt{10}}{4}$ in the direction given by ${\tan}^{- 1} \left(\frac{1}{3}\right)$

#### Explanation:

As the displacement for object A is $\left(2 , 1\right)$

and displacement for object B is $\left(5 , 2\right)$

relative displacement of B w.r.t. A is $\left(5 - 2 , 2 - 1\right)$ or $\left(3 , 1\right)$

as compared to $\left(0 , 0\right)$ at the start of $4$ seconds

Hence, relative velocity of object B from the perspective of object A is $\frac{3}{4} \hat{i} + \frac{1}{4} \hat{j}$

or $\sqrt{{\left(\frac{3}{4}\right)}^{2} + {\left(\frac{1}{4}\right)}^{2}} = \frac{\sqrt{10}}{4}$ in the direction given by ${\tan}^{- 1} \left(\frac{\frac{1}{4}}{\frac{3}{4}}\right) = {\tan}^{- 1} \left(\frac{1}{3}\right)$