Objects A and B are at the origin. If object A moves to #(-7 ,3 )# and object B moves to #(-6 ,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 #(-7  ,3  )# and object B moves to #(-6  ,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.

Charlotte Aaron · Accepted Answer

Given
#A" moves from "(0,0)->(-7,3)#
So displacement of A during 3 s #vecd_A=(-7hati+3hatj)m# Thus, the speed of A #vecv_A=vecd_A/3=(-7/3hati+hatj)m/s# #B" moves from "(0,0)->(-6,2)# Hence, B's displacement over 3 s #vecd_B=(-6hati+2hatj)m# Thus, the speed of A #vecv_B=vecd_A/3=-2hati+2/3hatj# Then the relative velocity of object B from the perspective of object A
#vecv_B-vecv_A=(-6+7/3)hati+(2/3-1)hatj#
#=-(11/3hati+1/3hatj)m/s#

Elena Albarran · Answer

undefined The relative velocity of object B from the perspective of object A is $ \vec{v}_{BA} = \vec{v}_B - \vec{v}_A $, where $ \vec{v}_A $ and $ \vec{v}_B $ are the velocities of objects A and B, respectively. Given the positions of the objects at different times, you can calculate their velocities using the displacement formula. Then, subtract the velocity of object A from the velocity of object B to find the relative velocity of B with respect to A.