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Determine the speed of block A if the end of the rope is pulled down with a speed of 4 m/s.

Step-by-step

Position Coordinates: By referring to Fig. a, the length of the cord written in terms of the position coordinates s_{A} and s_{B} is

s_{B}+s_{A}+2\left(s_{A}-a\right)=l
s_{B}+3 s_{A}=l+2 a

Time Derivative: Taking the time derivative of the above equation,
(+\downarrow)    v_{B}+3 v_{A}=0
Here, v_{B}=4 m/s. Thus,

4+3 v_{A}=0    v_{A}=-133 m/s=1.33 m/s \uparrow

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