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Statement

$1.5.1.$ The speed of the load $A$ is equal to $v_A$. What is the speed of load $B$?

Solution

Since the thread is rigid and inextensible, its length is preserved during the movement of the loads.

Let load $B$ rise a distance equal to $L$ in time $\Delta t$, then load $A$ will fall a distance $\frac{L}{2}$ in the same time.

This follows from the fact that on both sides of block $1$ the thread will lengthen by $\frac{L}{2}$, which means that the center of the block will fall the same distance. In this case, the length of the thread is preserved.

Then on one side

$$L = v_B \cdot \Delta t$$

and on the other

$$ \frac{L}{2} = v_A \cdot \Delta t $$

Therefore,

$$v_B \cdot \Delta t = 2v_A \cdot \Delta t$$

The speed of load $B$ is

$$\fbox{$v_B = 2v_A$}$$

Answer

$$v_B = 2v_A$$