A $78g,38-$cm$-$long rod hangs vertically on a frictionless, horizontal axle passing through its center. A $15$ g ball of clay traveling horizontally at $2\mathrm{.}0\frac{m}{s}$ 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.

$=$

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