Objects A and B are at the origin. If object A moves to #(-2 ,7 )# and object B moves to #(6 ,-5 )# 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.

1 Answer
P dilip_k
Mar 5, 2016

Initially both A and B were at origin O (0,0)
after 3sec A reaches at (-2,7) and B at (6,-5)
So displacement vector of A =#-2hati+7hatj# m
velocity vector of A, #vecV_A=1/3(-2hati+7hatj)# m/s
displacement vector of B =#6hati-5hatj#m
velocity vector of B, #vecV_B=1/3(6hati-5hatj)# m/s
So the relative velocity of B from the perspective of A is given by
#vecV_(BA) =vecV_B-vecV_A =1/3((6+2)hati-(5+7)hatj)#
# =1/3(8hati-12hatj)# m/s
#|vecV_(BA)| =1/3sqrt(8^2+12^2)=sqrt208/3=4.81ms^-1#

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