## Question:

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 $\uparrow$