Question

Objects A and B are at the origin. If object A moves to `(3 ,1 )` and object B moves to `(2 ,4 )` 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

(Using the positive Y-axis as North)
`1.118 m/s " at "47.16^@ W of N`

Explanation:

Distance after `8 s` between A and B
`color(white)("XXX")d=sqrt((3-2)^2+(1-4)^2)=sqrt(10)` (m)
Speed of B relative to A: `sqrt(10)/8 m/s ~~1.118 m/s`

If `theta` is the angle from A to B (relative to the Y-axis)
then `tan(theta)=(4-1)/(2-3)=-3`
`rArr theta~~137.16^@` (relative to the positive X-axis)
or
`color(white)("XXX")47.16^@` (relative to the Y-axis)