Gate $AB$ is $5m$ wide into the paper and opens to let freshwater out when the ocean tide is dropping. The hinge at $A$ is $0\mathrm{.}5m$ above the freshwater level. Neglect the gate weight.

The specific gravity $($S$)$ of seawater is $1\mathrm{.}025.$

$(1)$ Sketch the pressure distribution along both sides of the gate. Note important

$(2)$ points on the sketch.

At what ocean level $h$ will the gate first open?

$($Hint: you will need to solve a nonlinear equation using a calculator or using an iterative approach starting from an initial guess of e$.$g$.,h=4m.$ Please make sure to derive and clearly write down the equation to be solved even if you do not finish solving it$.)$