the Liquid Storage Corporation owns a very large, tall tank containing liquid.

the liquid level inside the tank, $h[m],$ is unknown because the tank is steel and thus opaque.

a small hole was punctured in the side of the tank, at a height $H[m].$ the liquid stream shooting out of the orifice lands a distance $L[m]$ from the tank.

note: a vent ensures the pressure in the headspace of the tank is atmospheric.

$($a$)$ according to Torricelli's law, what is the velocity of the liquid $v_x[\frac{m}{s}]$ shooting out of the side of the tank?

$($b$)$ how long does it take a packet of fluid shooting out of the tank to hit the ground? neglect air resistance.

$($c$)$ using your answers above, relate $H,h,$ and $L$ with an algebraic equation.

$($d$)$ suppose we observe $L=9\mathrm{.}97m$ and $H=4m.$ what is the liquid level $h$ inside the