During your summer internship for an aerospace company, you are asked to design a small research rocket. the rocket is to be launched from rest from the earth's surface and is to reach a maximum height of 940 m above the earth's surface. the rocket's engines give the rocket an upward acceleration of 16.0 m/s2 during the time t that they fire. after the engines shut off, the rocket is in free fall. ignore air resistance. what must be the value of t in order for the rocket to reach the required altitude?

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.