Objects A and B are at the origin. If object A moves to #(-6 ,-2 )# and object B moves to #(-5 ,-4 )# 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 · 2016-07-07T08:29:22

#v_"AB"=sqrt5/3 " "m/s#
#"please look over the animation"#

enter image source here

#vec a:"represents velocity of B from perspective of A"#
#u:"(red vector) represents velocity of A"#
#v=u:"represents velocity of B"#

#"note that "vec a=vec w-vec u#

enter image source here

#"you need to find the relative displacement"#
#"let "Delta x" be relative displacement"#
#"please look over the figure above"#

#Delta x=sqrt(AG^2+GB^2)#

#"or:"#

#A=(-6,-2)" ; "B=(-5,-4)#
#Delta x=sqrt((-5+6)^2+(-4+2)^2)#

#Delta x=sqrt(1^2+(-2)^2)=sqrt(1+4)=sqrt5#

#Delta t=3" "s#

#v_"AB"=(Delta x)/(Delta t)#

#v_"AB"=sqrt5/3 " "m/s#