An elastic loaded water balloon launcher fires balloons at an angle of 52°with the ground. If the initial velocity of the balloon is 25 m/s, determine a)how far away from the launcher will each balloon land when it just comes in contact with level ground once more?
b)How high above the ground is the balloon at 3 seconds?
c)How high above the ground is the balloon after it has traveled 40 meters?

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.