Find the velocity of block C.

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Solution

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)
$\Rightarrow v_{Q} = 6 m / s$

Considering pulley 2 which is fixed.
$∴ v_{E} = v_{D} = v_{Q} = 6 m / s$

Now consider pulley 3 which is moving
$v_{3} = \frac{v_{F} + v_{G}}{2} = v_{B}$
(here $v_{F} = v_{E} = 6 m / s$ )
$\Rightarrow 5 = \frac{- 6 + v_{G}}{2}$
(taking downward velocities positive and upward negative)
$\Rightarrow v_{G} = 16 m / s$

Since pulley 4 is also fixed,
$v_{J} = v_{I} = v_{H} = v_{G} = 16 m / s$
Therefore the velocity of block C is $16 m / s$

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