Answer
$\omega=20 rad/s$
$v_A=2ft/s$
Work Step by Step
The required velocity and angular velocity can be determined as follows:
$v_{C/B}=v_C-v_B$
$\implies v_C=v_B+v_{C/B}$
$\implies v_C=v_B+\omega r_{C/B}$
We plug in the known values to obtain:
$-4=8-0.6\omega$
This simplifies to:
$\omega=20 rad/s$
Similarly, for rack $A$ and gear $B$, we know that
$v_A=v_B+v_{A/B}$
$\implies v_A=v_B+\omega r_{A/B}$
We plug in the known values to obtain:
$v_A=8-(20)(0.3)=2ft/s$
