The ratio of masses of the Cylinder A to that of the cylinder B is 1:3 and the cylinder B has a mass of
9kg. Determine the speeds of both the cylinders after A moves upwards 4 m starting from rest. Neglect the mass of the cord and pulleys.

1) 5.76 ft/s, 11.5 ft/s
2) 9.55 ft/s, 5.3 ft/s
3) 3.54 ft/s, 9.8 ft/s
4) 5.30 ft/s, 6.2 ft/s

Kinematics: The speed of cylinder A and B can be related by using position coordinate equation
2S_A + S_B = l and 2DS_A +  DS_B = 0
DS_B = -2DS_A = -2(4) = 8m (downwards)
Also 2V_A + V_B = 0     --------------------------------(1)

Principle of work and energy: By considering the whole system, weight B acts in the direction of the displacement does positive work. Wieght A does negative work since it acts in the opposite direction to that of the displacement. Since block A and B are at rest initally, T₁ = 0.
Applying the conservation of energy principle we have:
T₁ + S U_1-2 = T₂
9(9.81)8 - 3(9.81)(2) = 1/2(9)(V_B)² + 1/2(3)(V_A)²
431.64 = 3(V_B)² + (V_A)²     ------------------------(2)

Solving equations (1) and (2) we have that
V_A = 5.76 m/s and also V_B = 11.52 m/s (down)

So the velocities of blocks A and B after A travels 4m are V_A = 5.76 m/s and V_B = 11.52 m/s respectively.