Consider the mechanism shown. $AB$ is $2.8$ $m$ long. $BC$ is $6.2$ $m$ long. The angle $\theta$ is $16.7$$^{\circ}$. $AB$ and $BC$ are currently at an angle of $90^{\circ}$. Peg $C$ is constrained to move along the $x$ direction. If peg $C$ is moving with velocity $8.1$ $m/s$ $i$, find $\omega_{BC}$. Give a positive response to indicate the rotation direction is counter-clockwise, or a negative response to indicate clockwise rotation.

$\omega_{BC}=$$rad/s$