Shown below is a sealed, square $($W by W$),$ container that is partially filled with water. The cart is resting on frictionless wheels. There is a U$-$tube manometer connected to the wall above the water line as shown. There is a rectangular slot of width W and height H that is cut into the side of the cart at depth l$\_3,$ near the bottom where the water is escaping as shown by the arrows. Assume H is relatively small compared with the other dimensions such that the problem is "quasi$-$steady". Assume in the manometer l$\_1=40$cm and l$\_2=22$cm$,$ and SG of the fluid is $13\mathrm{.}6.$ Assume l$\_3=0\mathrm{.}5$m$,$ W $=2$m$,$ and H$=0\mathrm{.}01$m$.$ A$)$ Calculate the time rate of change dl$/$dt$.$

B$)$ Calculate the reaction force R$\_1$ required to hold the container in place.