# Objects A and B are at the origin. If object A moves to (-6 ,-5 ) and object B moves to (-1 ,4 ) 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 1, 2016

$\setminus \vec{{v}_{A B}} = \left(- 6 , - 5\right) - \left(- 1 , 4\right) = \left(- 5 , - 9\right)$

#### Explanation:

Relative Velocities Rules:
[1] \vec{v_{AC}} = \vec{v_{AB}} + \vec{v_{BC}};
[2] $\setminus \vec{{v}_{A B}} = - \setminus \vec{{v}_{B A}}$

$\setminus \vec{{v}_{A B}}$ - Velocity of A relative to B,$\setminus q \quad \setminus \vec{{v}_{B C}}$ - Velocity of B relative to C,
$\setminus \vec{{v}_{A C}}$ - Velocity of A relative to C,

Taking ground as the reference frame C

$\setminus \vec{{v}_{A B}}$ - Velocity of A relative to B,
$\setminus \vec{{v}_{B g}} = \left(- 1 , 4\right)$ - Velocity of B relative to ground,
$\setminus \vec{{v}_{A g}} = \left(- 6 , - 5\right)$ - Velocity of A relative to ground,

$\setminus \vec{{v}_{A g}} = \setminus \vec{{v}_{A B}} + \setminus \vec{{v}_{B g}}$
$\setminus \vec{{v}_{A B}} = \setminus \vec{{v}_{A g}} - \setminus \vec{{v}_{B g}} = \left(- 6 , - 5\right) - \left(- 1 , 4\right) = \left(- 5 , - 9\right)$