Find the velocity of the hanging block if the velocities of the free ends of the rope are as indicated in the figure. Take the upward velocity to be positive.

The correct option is A $+\frac{3}{2}m/s$

Since pulley $1$ is fixed, $v_A=2m/s$ (upwards)
Since pulley $2$ is fixed, $v_B=1m/s$ (upwards)

Velocity of pulley $3$ $=\frac{v_A+v_B}{2}=\frac{3}{2}\text{m/s}$
Therefore velocity of the block = $v_3=\frac{3}{2}\text{m/s}$ upwards