$6-39$ A horizontal $4-$cm$-$diameter water jet with a velocity of $18\frac{m}{s}$ impinges normally upon a vertical plate of mass $750$ kg $.$ The plate rides on a nearly frictionless track and is initially stationary. When the jet strikes the plate, the plate begins to move in the direction of the jet. The water always splatters in the plane of the retreating plate. Determine $($a$)$ the acceleration of the plate when the jet first strikes it $($time $=0),($b$)$ the time it takes for the plate to reach a velocity of $9\frac{m}{s},$ and $($c$)$ the plate velocity $20$ s arer the je hirs strikes the plate. For simplicity, assume the velocity of the jet is increased as the cart moves such that the impulse force exerted by the water jet on the plate remains constant.

Ans. To check: a$)0\mathrm{.}543$m$/$s$^2$ b$)16\mathrm{.}6$ sec