# Objects A and B are at the origin. If object A moves to (-2 ,7 ) and object B moves to (6 ,-5 ) 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 5, 2016

Initially both A and B were at origin O (0,0)
after 3sec A reaches at (-2,7) and B at (6,-5)
So displacement vector of A =$- 2 \hat{i} + 7 \hat{j}$ m
velocity vector of A, ${\vec{V}}_{A} = \frac{1}{3} \left(- 2 \hat{i} + 7 \hat{j}\right)$ m/s
displacement vector of B =$6 \hat{i} - 5 \hat{j}$m
velocity vector of B, ${\vec{V}}_{B} = \frac{1}{3} \left(6 \hat{i} - 5 \hat{j}\right)$ m/s
So the relative velocity of B from the perspective of A is given by
${\vec{V}}_{B A} = {\vec{V}}_{B} - {\vec{V}}_{A} = \frac{1}{3} \left(\left(6 + 2\right) \hat{i} - \left(5 + 7\right) \hat{j}\right)$
$= \frac{1}{3} \left(8 \hat{i} - 12 \hat{j}\right)$ m/s
$| {\vec{V}}_{B A} | = \frac{1}{3} \sqrt{{8}^{2} + {12}^{2}} = \frac{\sqrt{208}}{3} = 4.81 m {s}^{-} 1$