$(37.$ Fluid "jetser"$-$M$.$ The October $1993$ Journal of Engineering Education gives an account of a competition in the Civil Engineering department at Oregot State University. There, "Students design and build a fluid jetser powered solely by water from a reservoir connected to a nozzle and mounted on a wheeled platform." A possible configuration for such a "fluid jetser" is shown in Fig. P$2\mathrm{.}37.$

Neglecting fluid friction, use Bernoulli's equation to derive an expression for $v($the exit velocity of the water, relative to the nozzle$)$ in terms of the current value of the height differential $($h$.$ If the cross$-$sectional area of the nozzle is and the density of water is $,$ give an expression for the mass flow rat $(m)$ hat is leaving the nozzle.

$\frac{d()}{}=-(-m(u+v))-F.$

Then perform a momentum balance on the moving jetser, $($s seen by a stationary observer.$)$ Hence, derive an expression for the acceleration $($du$/$dt$)$ in terms of any or all of $h,A,F($the drag force$),u,(M)($the current mass of the vehicle$),,$ and any physical constant$($s$)$ that you think are necessary.