A football is thrown at an angle of 30° above the ground and is in the air for a total of 1.93 s before it is caught (at the same height). If the football traveled a horizontal distance of 43 m
a) with what speed was the football thrown?
b) what max height would the football reach?

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.