# Who's In-volute?

Classical Mechanics Level pending

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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