DISCUSSION
This problem is a natural for the linear impulse-momentum equation. With this approach, it is recommended that you include the cart, the winch, the cable and block B in your system. With this choice of system, the cable tension force becomes internal and not needed in the impulse-momentum equation.
Recall out four-step plan:
Step 1: FBD - Draw an FBD of the total system (cart+winch+cable+B).
Step 2: Linear impulse/momentum - Carefully consider the FBD above. In which directions (if any) is linear momentum conserved?
Step 3: Kinematics - For Part (a), you will need to use the relative velocity equation of vB = vA + vB/A. In this equation, what is vB/A?
Step 4: Solve - Use your equations from Steps 3 and 4 to solve for the velocities requested.
Any questions??