what do I do with the $x$ which is unknown?

$\theta =\arctan\left(\frac{v_0}{xg}\pm \sqrt{\frac{v_0^2\left(v_0^2-2gk\right)}{x^2g^2}-1}\right)$

$S_0$ is the $y$ coordiante of our cannon, while $S(t)$ is our $y$ coordinate of the target. I get that $S(t) =-\frac{gx^2}{2v_0^2}\tan^2\theta +x\tan\theta - \frac{gx^2}{2v_0^2}+ S_0 - S(t) = 0$ we can write $S_0-S(t) = K$ for now, letting $u=\tan\theta$ since everything but $\theta$ is constants we have a second order polynomial with $K=m_1u+m_2u^2$ who has the solutions $u= \frac{-a\pm \sqrt{a^2+4kb}}{2b}$ implying that $\theta = \arctan\left(\frac{-a\pm \sqrt{a^2+4kb}}{2b}\right)$

I think i can get somewhere with this. The proper way would be to solve the integral then plug in $Q_{enc}$ into the gaussian and then solving for the electric field right?

I'm given a hint that we can find $k$ by solving $Q=\int \rho dV$ and that the Geometri of this problem makes it so that its a wise choice to work in spherical coordinates

My bad for being so confusing i translated the wrong problem. I want to find the electrical field $E$ given that $Q$ is evenly distributed over the volume of the sphere with radius $a$so that the electric charge density is proportional with the distance $r$ from the spheres centrum and i'm given that the $\rho_v=kr$ where $k$ is a constant

my $\rho$ or $\rho_s$ is the surface charge density

$E=\frac{r\rho}{3\epsilon}=>E=\frac{r^2k}{3\epsilon}$?

would it be $E=\frac{\frac{4}{3}\pi r^3 \rho}{\epsilon 4\pi r^2}$

if i were to find the electric field of it knowing that the radius is proportional.

@Triatticus That's the only information i'm given, besides that we have a Total charge $Q$ and i'm supposed to find the electrical field $E$ everywhere when ....$Q$ is evenly etc....