$(30$ points$)$ The tide gate opens automatically when the tidewater at B subsides, allowing the marsh at A to drain. The gate has a width of $2m.$

$($a$)$ Compute the magnitude of the resultant force on the lefthand side of the gate when the water level is $h=4m,$

$($b$)$ Compute the magnitude of the resultant force on the righthand side of the gate,

$($c$)$ Compute the moment about $D$ of the resultant force from part A

$($d$)$ Compute the moment about $D$ of the resultant force from part B

$($e$)$ For the water level $h=4m,$ determine the horizontal reaction at the smooth stop $C.$