Problem $4-$ yes it's rocket science

Have you ever launched a water rocket? The Aqua Pod kit lets you

turn a $2$L plastic bottle into a rocket. Check out this video. Basically

you fill it about $\frac{1}{3}$ full, pressurize the bottle and the air above it$,$ and

release the rocket. As the water shoots out, the rocket shoots upwards.

A simplified schematic of a water rocket is shown at right, and

additional parameters are given below.

$H_0=15cm$ initial water depth

$p_0=50=$i initial air pressure $(gage)$

$m_{\text{b}\text{o}\text{t}}=25g$ mass $of$ empty bottle

$V_w=0\mathrm{.}6L$ initial volume $of$ water

$A_{\text{b}\text{o}\text{t}}=0\mathrm{.}00785m^2$ cross$-$section area $of$ bottle

$K_{\text{o}\text{u}\text{t}}=0\mathrm{.}8$ exit loss coefficient

$(4\mathrm{.}1)$ Neglecting major losses $($since $\frac{L}{D}$ is small$),$ what is the velocity

of the water out of the bottle, initially?

Area mout $-$ v$.$uvusoi!

$(4\mathrm{.}2)$ What is the required force to hold the bottle stationary when it is first released? Neglect any friction

associated with the flow.

$(4\mathrm{.}3)$ Treating the downwards water momentum flux as a thrust force upwards, estimate the initial upwards

acceleration for the entire system