Mass of water reaching the plate per sec = $\frac{{dm}}{{dt}}$

$ = Av\rho = A({v_1} + {v_2})\rho $$ = \frac{V}{{{v_2}}}({v_1} + {v_2})\rho $

($v = {v_1}\, + \,{v_2}\, = $ velocity of water coming out of jet w.r.t. plate)

($A = $ Area of cross section of jet $ = \frac{V}{{{v_2}}}$)

$\therefore F = \frac{{dm}}{{dt}}v = \frac{V}{{{v_2}}}({v_1} + {v_2})\rho \times ({v_1} + {v_2})$ $ = \rho \left[ {\frac{V}{{{v_2}}}} \right]{({v_1} + {v_2})^2}$