# Objects A and B are at the origin. If object A moves to (-7 ,-5 ) and object B moves to (1 ,-1 ) 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.

Jun 16, 2016

${v}_{\text{AB"=sqrt5/2" }} \frac{m}{s}$

${v}_{\text{BA"=-sqrt5/2" }} \frac{m}{s}$

#### Explanation:

$\text{when the object moves from origin to the point of a the position}$ $\text{of its will have changed}$
$\text{figure above shows displacement of the object A}$

$\text{the figure above shows displacement of the object B}$

$\text{the relative displacement of B from perspective of A is shown in }$
$\text{figure}$

$\text{the relative displacement may be calculated using Pythagoras or}$
$\text{cosine laws}$

$\Delta s = \sqrt{{\left(1 + 7\right)}^{2} + {\left(- 1 + 5\right)}^{2}} = \sqrt{{\left(8\right)}^{2} + {\left(4\right)}^{2}} = \sqrt{64 + 16} = \sqrt{80}$
$\Delta s = \sqrt{80} = 4 \sqrt{5} \text{ } m$

${v}_{\text{AB}} = \frac{\Delta s}{\delta t}$

${v}_{\text{AB}} = \frac{4 \sqrt{5}}{8}$

${v}_{\text{AB"=sqrt5/2" }} \frac{m}{s}$

${v}_{\text{BA"=-sqrt5/2" }} \frac{m}{s}$