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"))#