Two sticky spheres are suspended from light ropes of length LL that are attached to the ceiling at a common point. Sphere AA has mass 2mm and is hanging at rest with its rope vertical. Sphere BB has mass mm and is held so that its rope makes an angle with the vertical that puts BB a vertical height HH above AA. Sphere BB is released from rest and swings down, collides with sphere AA, and sticks to it. In terms of H, H, what is the maximum height above the original position of A reached by the combined spheres after their collision?