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

1 Answer
Mar 4, 2016

Answer:

Object B moves away from object A with a speed of #1.202# #m/sec# in a direction given by #-33.7^o# relative to #x# axis.

Explanation:

As object A moves to #(-8,-2)# and object B moes to #(-5,-4)#, the distance between them after #3# seconds is

#sqrt((-5-(-8))^2+(-4-(-2))^2)# i.e. #sqrt(3^2+(-2)^2)# or

#sqrt(9+4)=sqrt13=3.606#

Hence object B moves away from object A with a speed of #3.606/3=1.202# #m/sec#.

Direction is given by #tan^-1((-4-(-2))/(-5-(-8)))=tan^-1(-2/3)=-33.7^o# relative to #x# axis