A horizontal plane supports a fixed vertical cylinder of radius \(R\) and a ball \(A\) attached to the cylinder by a horizontal thread \(AB\) of length \(l_0\). An initial velocity \(v_0\) is imparted to the ball as shown in the figure. The coefficient of restitution is \(e\). Find the time in which the velocity of the ball reduces to \(\frac {v_0}{16}\).

\(Details:\) There is no friction between the ball and the plane. Round off the answer to the closest integer.

\(1) l_0 = \frac {6}{\pi} m\)

\(2) v_0 = 5ms^{-1}\)

\(3) R = \frac {4}{\pi^2} m\)

\(4) e = \frac {1}{\sqrt2}\)

This is my first original problem on Brilliant. Please guide me if I haven't been able to follow the guidelines properly. :)

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