Answer
$v_O=0.667ft/s \rightarrow$
Work Step by Step
We can determine the required velocity as follows:
We know that
$v_{C/B}=v_C-v_B$
$\implies v_B=v_C\times \omega\times r_{B/C}$
$\implies 3\hat i=-4\hat i+(-\omega \hat k)\times (1.5+0.75\hat j)$
$\implies 3\hat i=(2.25\omega -4)\hat i$
This simplifies to:
$\omega=3.111 rad/s$
Now the relative motion between points $O$ and $C$ is given as
$v_O=v_C+v_{O/C}$
$\implies v_O=v_C+\omega \times r_{O/C}$
We plug in the known values to obtain:
$v_O=-4\hat i+(-3.111\hat k)(1.5\hat j)$
This simplifies to:
$v_O=0.667ft/s \rightarrow$
