Question

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.

Answer 1

`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)`