# Objects A and B are at the origin. If object A moves to (3 ,6 ) and object B moves to (6 ,-5 ) over 1 s, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.

Jul 30, 2017

${\vec{v}}_{B w . r . t A} = 3 \hat{i} - 11 \hat{j}$

#### Explanation:

${\vec{r}}_{i}$= initial displacement vector
${\vec{r}}_{j}$=final displacement vector
${\vec{r}}_{A}$=Displacement vector of A
${\vec{r}}_{B}$=Displacement vector of B
w.r.t=with respect to

${\vec{r}}_{i} = \vec{0}$
${\vec{r}}_{f} = 3 \hat{i} + 6 \hat{j}$
${\vec{r}}_{A} = {\vec{r}}_{f} - {\vec{r}}_{i}$
${\vec{r}}_{A} = 3 \hat{i} + 6 \hat{j}$

${\vec{r}}_{i} = \vec{0}$
${\vec{r}}_{f} = 6 \hat{i} - 5 \hat{j}$
${\vec{r}}_{B} = {\vec{r}}_{f} - {\vec{r}}_{i}$
${\vec{r}}_{B} = 6 \hat{i} - 5 \hat{j}$

${\vec{r}}_{B w . r . t A} = {\vec{r}}_{B} - {\vec{r}}_{A}$

${\vec{r}}_{B w . r . t A} = 3 \hat{i} - 11 \hat{j} \left(m\right)$

${\vec{v}}_{B w . r . t A} = \frac{{\vec{r}}_{B w . r . t A}}{t}$

${\vec{v}}_{B w . r . t A} = \frac{3 \hat{i} - 11 \hat{j} \left(m\right)}{1 s}$

${\vec{v}}_{B w . r . t A} = 3 \hat{i} - 11 \hat{j} \left(m \cdot {s}^{-} 1\right)$

$| {\vec{v}}_{B w . r . t A} | = \sqrt{130} m \cdot {s}^{-} 1$