$(40$P$)$ A mechanism converts rotational motion of the crank link into translational motion of the output slider which is constraint to move a long$-$inclined guide $DE.$ The crank link $AB$ rotates with a speed of $48ra\frac{d}{s}$ in clockwise direction. For the instant where link $AB$ is vertical, determine,

a$)$ the position and velocity of the slider with respect to point $A,$

b$)$ the angular position and velocity of link $BC.$

city $of$ link $BC.$

$r_1=180mm,r_2=60mm,r_3=290mm$