# A Projection Of Circular Proportions!

Classical Mechanics Level 5

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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