Objects A and B are at the origin. If object A moves to $(9 ,7 )$ and object B moves to $(-8 ,-1 )$ 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.

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Answer 1 · 2016-11-08T09:56:06

$(-17/3 "m/s", -8/3 "m/s")$

The velocity of A, $V_"A"$ is given by its displacement over the time taken.

$V_"A" = 1/(3"s") * [((9"m"), (7"m")) - ((0"m"), (0"m"))] = ((3 "m/s"), (7/3 "m/s"))$

Similarly, the velocity of B, $V_"B"$ is given by

$V_"B" = 1/(3"s") * [((-8"m"), (-1"m")) - ((0"m"), (0"m"))] = ((-8/3 "m/s"), (-1/3 "m/s"))$

In the frame of A, B looks as if it is traveling with velocity

$V_{"B rel A"} = V_"B" - V_"A"$

$= ((-8/3 "m/s"), (-1/3 "m/s")) - ((3 "m/s"), (7/3 "m/s"))$

$= ((-17/3 "m/s"), (-8/3 "m/s"))$

Objects A and B are at the origin. If object A moves to (9 ,7 )(9 ,7 ) and object B moves to (-8 ,-1 )(-8 ,-1 ) over 3 s3 s, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.