# Objects A and B are at the origin. If object A moves to (-7 ,3 ) and object B moves to (-6 ,2 ) 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.

Aug 9, 2016

Given
$A \text{ moves from } \left(0 , 0\right) \to \left(- 7 , 3\right)$
So displacement of A during 3 s

${\vec{d}}_{A} = \left(- 7 \hat{i} + 3 \hat{j}\right) m$

So velocity of A

${\vec{v}}_{A} = {\vec{d}}_{A} / 3 = \left(- \frac{7}{3} \hat{i} + \hat{j}\right) \frac{m}{s}$

$B \text{ moves from } \left(0 , 0\right) \to \left(- 6 , 2\right)$

So displacement of B during 3 s

${\vec{d}}_{B} = \left(- 6 \hat{i} + 2 \hat{j}\right) m$

So velocity of A

${\vec{v}}_{B} = {\vec{d}}_{A} / 3 = - 2 \hat{i} + \frac{2}{3} \hat{j}$

Then the relative velocity of object B from the perspective of object A
${\vec{v}}_{B} - {\vec{v}}_{A} = \left(- 6 + \frac{7}{3}\right) \hat{i} + \left(\frac{2}{3} - 1\right) \hat{j}$
$= - \left(\frac{11}{3} \hat{i} + \frac{1}{3} \hat{j}\right) \frac{m}{s}$