Objects A and B are at the origin. If object A moves to #(5, -1)# and object B moves to #(-7, 8)# 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, -1)# and object B moves to #(-7, 8)# 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.

Layla Ahmed · Accepted Answer

This one seems tougher than it really is. The two objects start together at a separation of #0# #m#, and end at a separation of #r=15# #m#, #3# #s# later. That means the relative velocity, #v=(Delta d)/(Delta t)=15/3=5# #ms^-1#.

To calculate the separation between the objects' final positions: #r=sqrt((x_2-x_1)^2+(y_2-y_1)^2)=sqrt((-7-5)^2+(8-(-1))^2)=sqrt(144+81)=15# #m#

Carson Alexander · 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. First, calculate the velocity vectors for both objects by dividing the displacement vectors by the time interval. Then, subtract the velocity vector of object A from the velocity vector of object B to obtain the relative velocity vector. Finally, find the magnitude of the relative velocity vector to get the relative velocity.