A$4.$ A U$-$shape channel covered by a lid of $500mm$ long hinged at the top is depicted in Fig. A$\mathrm{.}4.$ A horizontal water jet of $7mm$ diameter with velocity $10\frac{m}{s}$ strikes at $200mm$ vertically below the hinge on the lid and the water is deflected smoothly upward or downward along the lid. A force F$,$ is applied normally at the bottom of the lid causing it to deflect $30$ clockwise. Assuming that the weight of the lid is negligible, determine the magnitude of the force $F.$

$(10$ marks$)$