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
2SA + SB = l and 2DSA +  DSB = 0
DSB = -2DSA = -2(4) = 8m (downwards)
Also 2VA + VB = 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 U1-2 = T2
9(9.81)8 - 3(9.81)(2) = 1/2(9)(VB)2 + 1/2(3)(VA)2
431.64 = 3(VB)2 + (VA)2     ------------------------(2)

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

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