Objects A and B are at the origin. If object A moves to #(-6 ,-5 )# and object B moves to #(-1 ,12 )# 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
Sep 27, 2017

Answer:

#vecv_(BA)=(5/3hati+17/3hatj) m/s#

Explanation:

A moves Origin #(0,0)# to #(-6,-5)#
Displacement vector of A is
#vecd_A=(-6-0)hati+(-5-0)hatj#
#vecd_A=-6hati-5hatj#
time is 3 sec
Velocity vector of A
#vecv_A=vecd_A/t=(-6hati-5hatj)/3=-6/3hati-5/3hatj#

B moves Origin #(0,0)# to #(-1,12)#
Displacement vector of B is
#vecd_B=(-1-0)hati+(12-0)hatj#
#vecd_B=-1hati+12hatj#
time is 3 sec
Velocity vector of B
#vecv_B=vecd_B/t=(-1hati+12hatj)/3=-1/3hati+12/3hatj#

Relative Velocity of B from the perspective of A
#vecv_(BA)=vecv_B-vecv_A#
#vecv_(BA)=(-1hati+12hatj)/3-(-6hati-5hatj)/3#
#vecv_(BA)=(-1hati+12hatj-(-6hati-5hatj))/3#
#vecv_(BA)=(-1hati+12hatj+6hati+5hatj)/3#
#vecv_(BA)=(5hati+17hatj)/3=(5/3hati+17/3hatj) (m/s)#