Question

Objects A and B are at the origin. If object A moves to `(3 ,-2 )` and object B moves to `(2 ,9 )` over `5 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

Relative velocity of `B` with respect to `A` is `2.21 " m/s"` at an angle of `95.2^@` (relative to the positve X-axis)

Explanation:

After moving `A` to `(3,-2)` and `B` to `(2,9)`
from `A`'s perspective `B` has moved `<-1,11>`
for a distance of `sqrt((-1)^2+11^2) = sqrt(122)`
Since this apparent motion takes place over `5` seconds
the apparent speed is `sqrt(122)/5 " m/s"~~2.21 " m/s"`

The angle of this apparent motion, `theta` (relative to the positive X-axis) is such that `tan(theta)=11/(-1)`

`"arctan(-11/1) ~~1.66` (radians) `~~95.2^@`