$$Fill in the given values you have, and we'll solve for the missing variable.$=\frac{m}{V}$

$$	$=$	$\text{density}$
$m$	$=$	$\text{mass}$
$V$	$=$	$\text{volume}$

A rocket of mass $m$ traveling with speed $v_0$ along the $x$ axis suddenly shoots out fuel equal to one$-$third its mass,

perpendicular to the $x$ axis $($along the $y$ axis$)$ with speed $2v_0.$

Express the final velocity of the rocket in $i^{r,j},k^{***}$ notation.

Express your answer in terms of the variable $v_0$ and unit vectors hat$(A),$hat$(f),$ and $k^{{?}^{{?}^{?}}}.$