A $4\mathrm{.}00$ kg ball is dropped from a height of $11\mathrm{.}0$ m above one end of a uniform bar that pivots at its center. The bar has mass $5\mathrm{.}00$ kg and is $4\mathrm{.}00$ m in length. At the other end of the bar sits another $4\mathrm{.}00$ kg 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$.$ How high will the other ball go after the collision?