Objects A and B are at the origin. If object A moves to #(2 ,1 )# and object B moves to #(5 ,2 )# over #4 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 #(2  ,1   )# and object B moves to #(5  ,2  )# over #4  s#, what is the relative velocity of object B from the perspective of object A?

Nora Arzate · Accepted Answer

#sqrt10/4# in the direction given by #tan^(-1)(1/3)# As the displacement for object A is #(2,1)# and displacement for object B is #(5,2)# relative displacement of B w.r.t. A is #(5-2,2-1)# or #(3,1)# as compared to #(0,0)# at the start of #4# seconds Hence, relative velocity of object B from the perspective of object A is #3/4hati+1/4hatj# or #sqrt((3/4)^2+(1/4)^2)=sqrt10/4# in the direction given by #tan^(-1)((1/4)/(3/4))=tan^(-1)(1/3)#

Xavier Adame · Answer

undefined The relative velocity of object B from the perspective of object A is the difference between the velocity vectors of B and A.

Velocity of object A: (2 - 0, 1 - 0) / 4 = (2/4, 1/4) = (0.5, 0.25) m/s
Velocity of object B: (5 - 0, 2 - 0) / 4 = (5/4, 2/4) = (1.25, 0.5) m/s

Relative velocity of B with respect to A: (1.25 - 0.5, 0.5 - 0.25) = (0.75, 0.25) m/s