Objects A and B are at the origin. If object A moves to $(0 ,-2 )$ and object B moves to $(5 ,4 )$ over $8 s$ , what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.

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Answer 1 · 2016-08-19T21:36:27

$= ((5/8),(3/4))$ m/s

at $t = 0$ , $vec (OA) = vec (OB) = ((0),(0))$

So:
$vec ((AB)_0) = ((0),(0))$

At $t = 8$ ,
$vec ((AB)_8) = vec ((AO)_8) + vec ((OB)_8)$

$= - vec ((OA)_8) + vec ((OB)_8)$

$= -((0),(-2)) + ((5),(4)) = ((5),(6))$

from A's perspective $vec ((AB)_8)$ is the displacement of B from A at $t= 8$ , ie holding point A fixed.

so if

$vec (Delta r)_(AB)= ((5),(6))$ m

then
$vec v_(AB)= (vec (Delta r)_(AB))/(Delta t) = 1/8((5),(6))$

$= ((5/8),(3/4))$ m/s

Objects A and B are at the origin. If object A moves to (0 ,-2 )(0 ,-2 ) and object B moves to (5 ,4 )(5 ,4 ) over 8 s8 s, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.