Objects A and B are at the origin. If object A moves to #(-3 ,-8 )# and object B moves to #(-2 ,-1 )# 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
Oct 1, 2017

Answer:

#vecv_(BA)=(hati+7hatj)/3 (m/s)#

Explanation:

A moves #(0,0)# to #(-3,-8)# in 3 seconds
Displacement #OA=(-3-0)hati+(-8-0)hatj=-3hati-8hatj#
Velocity of A #vecv_A="displacement"/"time"#
#vecv_A=(-3hati-8hatj)/3#

B moves #(0,0)# to #(-2,-1)# in 3 seconds
Displacement #OB=(-2-0)hati+(-1-0)hatj=-2hati-1hatj#
Velocity of B #vecB_A="displacement"/"time"#
#vecv_B=(-2hati-1hatj)/3#

Velocity of B from perspective of A
#vecv_(BA)=vecv_B-vecv_A=(-2hati-1hatj)/3-((-3hati-8hatj)/3)#
#vecv_(BA)=(-2hati-1hatj+3hati+8hatj)/3=(hati+7hatj)/3 (m/s)#