Objects A and B are at the origin. If object A moves to #(5 ,-8 )# and object B moves to #(-4 ,2 )# 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.

Question

Objects A and B are at the origin.  If object A moves to #(5  ,-8  )# and object B moves to #(-4  ,2  )# 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.

Leo Abeyta · Accepted Answer

The relative velocity of #B# with respect to #A# is #= < -3, 10/3> ms^-1#

The absolute velocity of #A# is #v_A=1/3 <5,-8> = < 5/3,-8/3> ms^-1#

The absolute velocity of #B# is #v_B=1/3 <-4,2> = < -4/3,2/3> ms^-1#

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

#v_(B//A)=v_B-v_A= < -4/3,2/3> - < 5/3,-8/3>#

# = <-4/3-5/3, 2/3+8/3 >#

#= < -3, 10/3> ms^-1#

Layla Ahmed · Answer

undefined The relative velocity of object B from the perspective of object A is calculated by subtracting the velocity of object A from the velocity of object B. Given the positions of object A and object B at different times, we can calculate their velocities by dividing the displacement by the time taken. Then, subtract the velocity of object A from the velocity of object B to find the relative velocity.

Velocity of object A = [(5 - 0) m / 3 s, (-8 - 0) m / 3 s] = [5/3 m/s, -8/3 m/s]

Velocity of object B = [(-4 - 0) m / 3 s, (2 - 0) m / 3 s] = [-4/3 m/s, 2/3 m/s]

Relative velocity of object B from the perspective of object A = Velocity of B - Velocity of A
= [(-4/3) - (5/3) m/s, (2/3) - (-8/3) m/s]
= [-3 m/s, 10/3 m/s]