Find the velocity of the hanging block if the | vedclass

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(B) Let the velocity of the hanging block be $v_B$ in the upward direction.Using the principle of constrained motion for the pulley system, the sum of

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$\frac{3}{2} \, m/s \downarrow$

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(B) Let the velocity of the hanging block be $v_B$ in the upward direction.Using the principle of constrained motion for the pulley system, the sum of the velocities of the rope segments connected to the movable pulley must be related to the velocity of the pulley itself.Taking upward as positive, the velocities of the two segments of the rope supporting the movable pulley are $-2 \, m/s$ (since the left end moves left, the segment length increases) and $-1 \, m/s$ (since the right end moves down, the segment length increases).Applying the constraint equation: $v_B = \frac{v_1 + v_2}{2}$.Here, $v_1 = -2 \, m/s$ and $v_2 = -1 \, m/s$ (considering the directions relative to the pulley).Actually, using the string constraint method: $v_{pulley} = \frac{v_{left} + v_{right}}{2}$.$v_B = \frac{(-2) + (-1)}{2} = -1.5 \, m/s$.The negative sign indicates that the block moves downwards.Therefore, the velocity of the block is $\frac{3}{2} \, m/s \downarrow$.

Find the velocity of the hanging block if the velocities of the free ends of the rope are as indicated in the figure.

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