A $2\mathrm{.}30$ kg solid, uniform ball of radius $0\mathrm{.}180$ m is released from rest at point $A$ in the figure below, its center of gravity a distance of $1\mathrm{.}80$ m above the ground. The ball rolls without slipping to the bottom of an incline and back up to point B where it is launched vertically into the air. The ball then rises to its maximum height $h_{\text{m}\text{a}\text{x}}$ at point $C.$

HINT

$($a$)$ At point $B,$ find the ball's translational speed $v_B($in $\frac{m}{s}).$

$\frac{m}{s}$

$($b$)$ At point $B,$ find the ball's rotational speed ${}_B($in rad$/$s$).$

$ra\frac{d}{s}$

$($c$)$ At point $C,$ find the ball's rotational speed ${}_C($in rad$/$s$).$

$ra\frac{d}{s}$

$($d$)$ At point $C,$ find the maximum height $h_{\text{m}\text{a}\text{x}}$ of the ball's center of gravity $($in m $).$

$$ m