"rocket man" has a propulsion unit strapped to his back. he starts from rest on the ground, fires the unit, and accelerates straight upward. at a height of 15 m, his speed is 4.8 m/s. his mass, including the propulsion unit, has the approximately constant value of 135 kg. find the work done by the force generated by the propulsion unit. (neglect air resistance.)

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.