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