Question

Find the velocity of block C.

Answer 1

Considering pulley 1 which is moving
$v_1=\frac{v_P+v_Q}{2}=v_A$
(point P is not moving, therefore $v_P=0$)
$\Rightarrow 3=\frac{0+v_Q}{2}$
(taking downward velocities positive and upward negative)
$\Rightarrow v_Q=6m/s$

Considering pulley 2 which is fixed.
$\therefore v_E=v_D=v_Q=6m/s$

Now consider pulley 3 which is moving
$v_3=\frac{v_F+v_G}{2}=v_B$
(here $v_F=v_E=6m/s$)
$\Rightarrow 5=\frac{-6+v_G}{2}$
(taking downward velocities positive and upward negative)
$\Rightarrow v_G=16m/s$

Since pulley 4 is also fixed,
$v_J=v_I=v_H=v_G=16m/s$
Therefore the velocity of block C is $16m/s$