PROBLEM $15\mathrm{.}184$

The bowling ball shown rolls without slipping on the horizontal $xz$ plane with an angular velocity $={}_{x}i+{}_{?}$

$uj+{}_{z}k.$ Knowing that $v_A=(4\mathrm{.}8\frac{m}{s})i-(4\mathrm{.}8\frac{m}{s})j+(3\mathrm{.}6\frac{m}{s})k$ and $v_D=(9\mathrm{.}6\frac{m}{s})i+(7\mathrm{.}2\frac{m}{s})k$ determine $(a)$ the angular velocity of the bowling ball, $($b$)$ the velocity of its center $C.$