$(5)$ A $50$ mm diameter jet having a velocity of $25\frac{m}{s},$ strikes a flat plate, the normal of which is inclined at $30$ to the axis of the jet. Calculate the normal force exerted on the plate $($a$)$ when the plate is stationary, $($b$)$ when the plate is moving with a velocity of $10\frac{m}{s}$ in the direction of the jet, $($c$)$ when the plate is moving with a velocity of $8\frac{m}{s}$ parallel to itself and in the direction of the normal to its surface. Find also the work done and the efficiency of the jet when the plate is moving.

$(20$ Marks$)$

$($c$)$