A $75$ gg $,31-$cmcm$-$long rod hangs vertically on a frictionless, horizontal axle passing through its center. A $10$ gg ball of clay traveling horizontally at $2\mathrm{.}0$ m$/$sm$/$s hits and sticks to the very bottom tip of the rod.

To what maximum angle, measured from vertical, does the rod $($with the attached ball of clay$)$ rotate? $$

Express your answer to two significant figures and include the appropriate units.