$(15$ points, Estimated time $20$min $)$ Water flows past a partially opened sluice gate, reaching

a height of $4ft$ some distance downstream.

a$.$ What is the magnitude and direction

of the force on the gate?

b$.$ What is the magnitude and direction

of force if the sluice gate closes?

Assume no water is downstream of

the gate in this scenario, and it

remains $6ft$ high upstream.

${}_{\text{w}\text{a}\text{t}\text{e}\text{r}}=1\mathrm{.}94\frac{\text{s}\text{l}\text{u}\text{g}}{ft}$

${}_{\text{w}\text{a}\text{t}\text{e}\text{r}}=62\mathrm{.}4\frac{lb}{f{t}^3}$