$15\mathrm{.}6\mathrm{.}2$ Shown is a four bar mechanism OABQ for a wrapping

machine. OA and QB rotate around fixed points O and Q

that are spaced $400$ mm from one another.

$OA=75mm$;$AB=300mm$;$BQ=100mm$

At the instant that the mechanism is considered, OA makes

an angle of $30$ with OQ and it rotates clockwise at $12s^{-1}.$

Calculate:

$($a$)$ the velocity $($including direction$)$ of C on A $,$

$100$ mm from $A.$

$($b$)$ the angular velocity of link $AB.$