Objects A and B are at the origin. If object A moves to #(-7 ,2 )# and object B moves to #(-5 ,-6 )# over #2 s#, what is the relative velocity of object B from the perspective of object A?

Question

Objects A and B are at the origin.  If object A moves to #(-7  ,2  )# and object B moves to #(-5  ,-6  )# over #2  s#, what is the relative velocity of object B from the perspective of object A?

Nathan Ashcroft · Accepted Answer

The relative velocity is #= < 1, -4> ms^-1 #

The time is #t=2s#

The absolute velocity of #A# is #v_A=1/2* <-7, 2> = <-7/2, 1>#

The absolute velocity of #B# is #v_B=1/2* <-5, -6> = <-5/2, -3>#

The relative velocity of #B# with respect to #A# is

#v_(B//A)=v_B-v_A#

#= <-5/2, -3> - <-7/2, 1>#

#= <-5/2-(-7/2), -3-(1) >#

#= < 1, -4> ms^-1#

William Audy · Answer

undefined To find the relative velocity of object B from the perspective of object A, subtract the velocity of object A from the velocity of object B.

The velocity of object A is the displacement of object A divided by the time taken: 
Velocity of A = ((-7 - 0), (2 - 0)) / 2 = (-7/2, 1).

The velocity of object B is the displacement of object B divided by the time taken: 
Velocity of B = ((-5 - 0), (-6 - 0)) / 2 = (-5/2, -3).

Relative velocity of B from the perspective of A = Velocity of B - Velocity of A = ((-5/2) - (-7/2), (-3) - 1) = (1/2, -4).