$6\mathrm{.}61$ Many recreation facilities use inflatable "bubble" structures. A tennis bubble to enclose four courts is shaped roughly as a circular semicylinder with a diameter of $50$ ft and a length of $50$ ft $.$ The blowers used to inflate the structure can maintain the air pressure inside the bubble at $0\mathrm{.}75$ in $.$ of water above ambient pressure. The bubble is subjected to a wind that blows at $35$ mph in a direction perpendicular to the axis of the semicylindrical shape. Using polar coordinates, with angle $$ measured from the ground on the upwind side of the structure, the resulting pressure distribution may be expressed as

$\frac{p-p_{}}{\frac{1}{2}{V}_{}^2}=1-4si{n}^2$

where $p$ is the pressure at the surface, $p_{}$ the atmospheric pressure, and $V_w$ the wind speed. Determine the net vertical force exerted on the structure.