Question

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

Treating the positive X-axis as North,
`color(white)("XXX")"approximately "4.38 m/(sec)" at "8.75^@ N" of "W`

Explanation:

The distance between points A and B has increased from `0` meters to
`color(white)("XXX")sqrt((5-(-8))^2+(1-(-1))^2)=sqrt(173)~~13.15` meters
for an average speed of
`color(white)("XXX")(sqrt(173) m)/(3 sec) ~~4.38 (m)/(sec)`

Relative to A, B has moved `13` meters East and `2` meters North.
If `theta` is the angle North of due East for B's movement relative to A then
`color(white)("XXX")tan(theta)=2/13`

`color(white)("XXX")rArr theta = arctan(2/13)~~8.75^@`

(Remember that velocity must always include a direction as well as a speed).