## Question:

If the end of the cable at A is pulled down with a speed of 2 m/s, determine the speed at which block B rises.

## Step-by-step

Position-Coordinate Equation: Datum is established at fixed pulley D. The
position of point A, block B and pulley C with respect to datum are ${s}_{A}$ , ${s}_{B}$ , and ${s}_{C}$ respectively. Since the system consists of two cords, two position-coordinate
equations can be derived.

(${s}_{A}$${s}_{C}$) + (${s}_{B}$${s}_{C}$) + ${s}_{B}$ =${l}_{1}$

${s}_{B}$${s}_{C}$ = ${l}_{2}$

${s}_{A}$ + 4${s}_{B}$  = ${l}_{1}$ = 2${l}_{2}$

Time Derivative: Taking the time derivative of the above equation yields

${v}_{A}$ + 4${v}_{B}$ = 0

since  ${v}_{A}$ = 2 m/s

($+\downarrow$ )                           2 + 4${v}_{B}$ = 0

${v}_{B}$ = -0.5 m/s = 0.5 m/s $\uparrow$