Question

Objects A and B are at the origin. If object A moves to `(-7 ,-5 )` and object B moves to `(1 ,-1 )` over `8 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

`v_"AB"=sqrt5/2" "m/s`

`v_"BA"=-sqrt5/2" "m/s`

Explanation:

`"when the object moves from origin to the point of a the position"` `"of its will have changed"`
`"figure above shows displacement of the object A"`

`"the figure above shows displacement of the object B"`

`"the relative displacement of B from perspective of A is shown in "`
`"figure"`

`"the relative displacement may be calculated using Pythagoras or"`
`"cosine laws"`

`Delta s=sqrt((1+7)^2+(-1+5)^2)=sqrt((8)^2+(4)^2)=sqrt(64+16)=sqrt(80)`
`Delta s=sqrt 80=4sqrt5 " "m`

`v_"AB"=(Delta s)/(delta t)`

`v_"AB"=(4sqrt5)/8`

`v_"AB"=sqrt5/2" "m/s`

`v_"BA"=-sqrt5/2" "m/s`