# Objects A and B are at the origin. If object A moves to (-3 ,-8 ) and object B moves to (-2 ,-1 ) 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.

Oct 1, 2017

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

#### Explanation:

A moves $\left(0 , 0\right)$ to $\left(- 3 , - 8\right)$ in 3 seconds
Displacement $O A = \left(- 3 - 0\right) \hat{i} + \left(- 8 - 0\right) \hat{j} = - 3 \hat{i} - 8 \hat{j}$
Velocity of A ${\vec{v}}_{A} = \text{displacement"/"time}$
${\vec{v}}_{A} = \frac{- 3 \hat{i} - 8 \hat{j}}{3}$

B moves $\left(0 , 0\right)$ to $\left(- 2 , - 1\right)$ in 3 seconds
Displacement $O B = \left(- 2 - 0\right) \hat{i} + \left(- 1 - 0\right) \hat{j} = - 2 \hat{i} - 1 \hat{j}$
Velocity of B ${\vec{B}}_{A} = \text{displacement"/"time}$
${\vec{v}}_{B} = \frac{- 2 \hat{i} - 1 \hat{j}}{3}$

Velocity of B from perspective of A
${\vec{v}}_{B A} = {\vec{v}}_{B} - {\vec{v}}_{A} = \frac{- 2 \hat{i} - 1 \hat{j}}{3} - \left(\frac{- 3 \hat{i} - 8 \hat{j}}{3}\right)$
${\vec{v}}_{B A} = \frac{- 2 \hat{i} - 1 \hat{j} + 3 \hat{i} + 8 \hat{j}}{3} = \frac{\hat{i} + 7 \hat{j}}{3} \left(\frac{m}{s}\right)$