$5\mathrm{.}2\mathrm{.}10$ Water flows steadily from a tank mounted on a cart, as shown in Fig. P$5\mathrm{.}2\mathrm{.}10.$ After the water jet leaves the nozzle of the tank, it falls and strikes a vane attached to another cart. The cart's wheels are frictionless, and the fluid is inviscid. $($a$)$ Determine the speed of the water leaving the tank, $V_1,$ and the water speed leaving the cart, $V_{2^{\text{'}}}($b$)$ Determine the tension in rope $A.($c$)$ Determine the tension in rope $B.$