Prob. $2\mathrm{.}52[$Ans: $6288$ lb$].$

$2\mathrm{.}52$ A gate having the cross section shown in Fig. P$2\mathrm{.}52$ closes an opening $5ft$ wide and $4ft$ high in a water reservoir. The gate weighs $400lb,$ and its center of gravity is $1ft$ to the left of $AC$ and $2ft$ above $BC.$ Determine the horizontal reaction that is developed on the gate at $C.$