A Projection Of Circular Proportions!

Consider a circle of radius 50 units, with a point sized object affixed to it at \(A\). The circle rotates with angular velocity \(\omega\), through an angle \(\theta\), when, after a time \(t\), it stops almost immediately. The object is projected should be projected in such a way that it falls tangentially on the other side of the circle, through the horizontal passing through the point of projection. If \(\omega =\frac{\pi}{5}\) radians per second, and \(g=9.8\) units per second, find the maximum of \(t\), such that the above projection occurs. Round to the nearest hundredth.

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