$2.$ During a storm, water levels rise dramatically in a drinking water reservoir $($surface area $=355$acres aka $1\mathrm{.}55\backslash$times $10\text{'}11*).$ Inflow to this reservoir comes from stormwater runoff from a $15,000$ acre $($aka $6\mathrm{.}53\backslash$times $10*$ it$*$ watershed upstream of the reservoir. Outflow from this reservoir is released via a $50$ ft wide rectangular spillway channel. The velocity profile of flow in this spillwaychannel can be described by the equation v $=3600$y$,$ where vis the velocity in ft$/$hr and y is thedepth of water in the channel in feet. At one point during the storm, runoff is generated at an average rate of $0\mathrm{.}5$ in$/$hr across the entire upstream watershed area. At the same time, water is $4$ ft deep in the spillway. At this moment, how quickly are water levels rising in the reservoir $($in ft$/$hr$)?$