Little Timmy, mass 25 kg, runs at 5 m/s toward a chair swing, mass 12 kg. The swing is connected to a horizontal pole by a virtually massless and frictionless tether of length 3.2 m. 

(A) Find a relationship between the velocity of the swing at its lowest point and the maximum angle of the swing. (Define your gravitational potential energies carefully and conveniently.) 

(B) Little Timmy, keeping his initial velocity, leaps into the swing. What maximum angle does the swing (with Little Timmy in it) reach? WARNING: Little Timmy's velocity may not be the starting velocity of the swing.