A $6\mathrm{.}00kg$ ball is dropped from a height of $11\mathrm{.}0m$ above one end of a uniform bar that pivots at its center. The bar has mass $7\mathrm{.}00kg$ and is $4\mathrm{.}00m$ in length. At the other end of the bar sits another $6\mathrm{.}00kg$ ball, unattached to the bar. The dropped ball sticks to the bar after the collision. Assume that the bar is horizontal when the dropped ball hits it$.$

Part A

How high will the other ball go after the collision?

Express your answer with the appropriate units.

$h=$

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