Problem $06\mathrm{.}022$E $-$ Water jet against a vertical plate on wheels

A horizontal water jet impinges against a vertical flat plate at $32f\frac{t}{s}$ and splashes off the sides in the vertical plane. If a horizontal force of $500$ lbf is required to hold the plate against the water stream, determine the volume flow rate of the water. Take the density of water to be $62\mathrm{.}4lb\frac{m}{f}{t}^3.($Round the final answer to two decimal places.$)$

The volume flow rate of the water is $f\frac{t^3}{s}$