A student decides to conduct an experiment. He drops one ball from a balcony located 12.3 m above the ground and throws down a second ball at 6.35 m/s from a balcony located 25.0 m above the ground. Determine the velocity of each ball as it strikes the ground.

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.