(10 points) A 100g steel ball and a 200g steel ball each hang from 2.0 m long strings. At rest, the balls hang side by side, barely touching. The 100g ball is pulled to the left until the angle between its string and the vertical is 55 degrees. The 200g ball is pulled to a 55 degree angle in the opposite direction, to the right. The balls are then released, collide at the bottom, and then rebound upwards. Assuming the coefficient of restitution of the collision is 0.7, find the height each ball rises after the collision.