Question

Objects A and B are at the origin. If object A moves to `(-5 ,2 )` and object B moves to `(-1 ,-8 )` over `4 s`, what is the relative velocity of object B from the perspective of object A?

Answer 1

Relative velocity (approximately): `color(green)(2.7)` units/sec at an angle of `color(green)(-68.2^@)`

Explanation:

Here is a graph of the resultant positions:

The relative displacement of `B` with respect to `A` is
`color(white)("XXX")4 " units horizontally"` and
`color(white)("XXX")-10 " units vertically"`.

The angle of displacement (to `B` relative to `A`) is therefore
`color(white)("XXX")arctan((-10)/4)~~-1.19028995" (radians)" ~~-68.19859051^@`
(calculator used for this)

The distance from `A` to `B` (using the Pythagorean Theorem) is
`color(white)("XXX")sqrt(4^2+(-10)^2)=sqrt(116)=2sqrt(29)" units"`

Since this distance was covered over a period of `4` sec.
the average speed must be `(2sqrt(29))/4 " units/sec" ~~2.69258..." units/sec."`

velocity is a combination of speed and angle.