# Pulley System Speed Analysis Given: - The end of the cable at **A** is pulled down at a speed of **5 m/s**. - We need to determine the **speed which block B rises**. ## 1: the Pulley From the: - The is a **simple movable** setup. - Pulling the cable at **A** down increases the total cable length on one side, which **lifts block B**. ## Step 2: Relationship Between Cable Movement and Block B Let: - \( V_A \) = speed at which end A moves down (\( 5 \) m/s, downward is positive) - \( V_B \) = speed at which block B moves up (upward is positive) In a movable pulley with **two segments supporting block B**: - For every unit length you pull down at A, block B rises by half that amount. ### Equation: \[ V_A = 2 V_B \] ## Step 3: Solve for \( V_B \) Given \( V_A = 5 \) m/s downward, \[ 5 = 2 V_B \\ V_B = \frac{5}{2} = 2.5 \ \text{m/s} \] ## Step 4: Direction Since pulling A down lifts B up: - **Block B rises at 2.5 m/s upward.** --- ## **Final Answer** \[ \boxed{2.5 \ \text{m/s upward}} \] Block B rises at **2.5 m/s upward** when the end at A is pulled down at 5 m/s.