As shown in the figure, block 'A' placed on a horizontal surface is moving horizontally with a speed of $10\text{ ms}^{-1}$. The speed of hanging block 'B' at the given instant of time is:
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For any string-constraint system where a block moves horizontally with speed $v$, the velocity of the string along its length is always $v \cos\theta$.
This directly equals the speed of the hanging block.
Step 1: Identify the constraint. Block A pulls the string horizontally while block B hangs from the other end over a pulley. Because the string is inextensible, only the component of A's velocity along the string direction actually shortens the string and lifts B. Step 2: Resolve the velocity. If the string from A to the pulley makes an angle $\theta$ with the direction A is moving, the speed at which that side of the string shortens is $v_A\cos\theta$, and this must equal the speed of B, $v_B = v_A\cos\theta$. Step 3: Use the geometry of the setup. The figure fixes this angle at $60^\circ$, so $\cos\theta = \frac{1}{2}$. Step 4: Compute the answer. \[ v_B = 10\text{ ms}^{-1}\times\frac{1}{2} = 5\text{ ms}^{-1} \] \[ \boxed{v_B = 5\text{ ms}^{-1}} \]
