# Objects A and B are at the origin. If object A moves to (-6 ,-5 ) and object B moves to (-1 ,12 ) 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.

Sep 27, 2017

${\vec{v}}_{B A} = \left(\frac{5}{3} \hat{i} + \frac{17}{3} \hat{j}\right) \frac{m}{s}$

#### Explanation:

A moves Origin $\left(0 , 0\right)$ to $\left(- 6 , - 5\right)$
Displacement vector of A is
${\vec{d}}_{A} = \left(- 6 - 0\right) \hat{i} + \left(- 5 - 0\right) \hat{j}$
${\vec{d}}_{A} = - 6 \hat{i} - 5 \hat{j}$
time is 3 sec
Velocity vector of A
${\vec{v}}_{A} = {\vec{d}}_{A} / t = \frac{- 6 \hat{i} - 5 \hat{j}}{3} = - \frac{6}{3} \hat{i} - \frac{5}{3} \hat{j}$

B moves Origin $\left(0 , 0\right)$ to $\left(- 1 , 12\right)$
Displacement vector of B is
${\vec{d}}_{B} = \left(- 1 - 0\right) \hat{i} + \left(12 - 0\right) \hat{j}$
${\vec{d}}_{B} = - 1 \hat{i} + 12 \hat{j}$
time is 3 sec
Velocity vector of B
${\vec{v}}_{B} = {\vec{d}}_{B} / t = \frac{- 1 \hat{i} + 12 \hat{j}}{3} = - \frac{1}{3} \hat{i} + \frac{12}{3} \hat{j}$

Relative Velocity of B from the perspective of A
${\vec{v}}_{B A} = {\vec{v}}_{B} - {\vec{v}}_{A}$
${\vec{v}}_{B A} = \frac{- 1 \hat{i} + 12 \hat{j}}{3} - \frac{- 6 \hat{i} - 5 \hat{j}}{3}$
${\vec{v}}_{B A} = \frac{- 1 \hat{i} + 12 \hat{j} - \left(- 6 \hat{i} - 5 \hat{j}\right)}{3}$
${\vec{v}}_{B A} = \frac{- 1 \hat{i} + 12 \hat{j} + 6 \hat{i} + 5 \hat{j}}{3}$
${\vec{v}}_{B A} = \frac{5 \hat{i} + 17 \hat{j}}{3} = \left(\frac{5}{3} \hat{i} + \frac{17}{3} \hat{j}\right) \left(\frac{m}{s}\right)$