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 \(50 \mathrm{ft}\) and a length of \(50 \mathrm{ft}\). The blowers used to inflate the structure can maintain the air pressure inside the bubble at \(0.75 \mathrm{in}\). of water above ambient pressure. The bubble is subjected to a wind that blows at \(35 \mathrm{mph}\) in a direction perpendicular to the axis of the semicylindrical shape. Using polar coordinates, with angle \(\theta\) measured from the ground on the upwind side of the structure, the resulting pressure distribution may be expressed as

\[\frac{p-p_{\infty}}{\frac{1}{2} ho V_{\infty}^{2}}=1-4 \sin ^{2} \theta\]

where \(p\) is the pressure at the surface, \(p_{\infty}\) the atmospheric pressure, and \(V_{w}\) the wind speed. Determine the net vertical force exerted on the structure.