Question

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.

Answer 1

`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)`