Objects A and B are at the origin. If object A moves to #(-7 ,-5 )# and object B moves to #(1 ,-1 )# 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.

1 Answer
Jun 16, 2016

Answer:

#v_"AB"=sqrt5/2" "m/s#

#v_"BA"=-sqrt5/2" "m/s#

Explanation:

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#"when the object moves from origin to the point of a the position"# #"of its will have changed" #
#"figure above shows displacement of the object A"#

enter image source here

#"the figure above shows displacement of the object B"#

enter image source here

#"the relative displacement of B from perspective of A is shown in "#
#"figure"#

#"the relative displacement may be calculated using Pythagoras or"#
#"cosine laws"#

#Delta s=sqrt((1+7)^2+(-1+5)^2)=sqrt((8)^2+(4)^2)=sqrt(64+16)=sqrt(80)#
#Delta s=sqrt 80=4sqrt5 " "m#

#v_"AB"=(Delta s)/(delta t)#

#v_"AB"=(4sqrt5)/8#

#v_"AB"=sqrt5/2" "m/s#

#v_"BA"=-sqrt5/2" "m/s#

enter image source here