# 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?

Mar 24, 2017

Relative velocity (approximately): $\textcolor{g r e e n}{2.7}$ units/sec at an angle of $\textcolor{g r e e n}{- {68.2}^{\circ}}$

#### 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 $\frac{2 \sqrt{29}}{4} \text{ units/sec" ~~2.69258..." units/sec.}$

velocity is a combination of speed and angle.