The motor at C winds the cable with a constant speed vC$=4$m$/$sv$\_$C $=4\backslash ,\backslash$text$\{$m$/$s$\}$vC$=4$m$/$s$.$

The motor at D winds the cable with a constant acceleration aD$=8$m$/$s$2$a$\_$D $=8\backslash ,\backslash$text$\{$m$/$s$\}^2$aD$=8$m$/$s$2.$

Given that vD$=0$m$/$sv$\_$D $=0\backslash ,\backslash$text$\{$m$/$s$\}$vD$=0$m$/$s at t$=0$st $=0\backslash ,\backslash$text$\{$s$\}$t$=0$s$,$ determine:

$($a$)$ The time required for block A to rise by $3$ m$.$

$($b$)$ The relative velocity of block A with respect to block B when this occurs.