$(25$ pts$)$ Load B is connected to a double pulley by one of the two inextensible cables shown. The motion of the pulley is controlled by cable C $,$ which has a constant acceleration of $7in\frac{.}{s}2$ and an initial velocity of $10i\frac{n}{s},$ both directed to the right. Determine $($a$)$ the number of revolutions executed by the pulley in $2$ s $,($b$)$ the velocity and change in position of the load B after $2$ s $.$