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

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)