A 17 ft ladder is leaning against a wall and sliding towards the floor. The top of the ladder is sliding down the wall at a rate of 6 ft/sec. How fast is the base of the ladder sliding away from the wall when the base of the ladder is 15 ft from the wall?

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.