sure.
In this problem we actually needn’t consider velocity of point O (because OB is given as 3\space \text{m}, so apparently this length is fixed). But the Damir’s solution (without considering this velocity) is correct. Just go into frame of reference where both O and A are motionless. It turns out that the whole Universe except the disc rotates at angular velocity -\vec \omega with respect to O, so
\vec v_B ' = -\vec\omega \times \vec x \quad \Rightarrow \quad|\vec v_B'| = v_A \frac{x}{R}.
p.s. i spent much time trying to give more rigour and general solution but then realized an easier one.