Competition billiard balls and tables need to adhere to strict standards (see the Billiard Congress of America for standards in the United States). Specifically, billiard balls must weigh between 5.5 and 6 oz, and they must be 2.25\pm 0.005 in. in diameter. Professional billiard players can easily impart to a ball a speed of 20 mph. Assume the tolerance on the ball diameter to be 1/100 in. instead of 5/1000 in. and determine the outcome of the collision between (a) a 2:26 in: diameter ball traveling at 20 mph with a stationary 2.24 in. diameter ball (i.e., each ball is at the extreme limit of tolerance relative to the nominal diameter) and (b) a 2.24 in. diameter ball traveling at 20 mph with a stationary 2.26 in. diameter ball. Assume that the COR e = 1 and that the weights of the two balls are identical. Furthermore, assume that the contact between the balls and the table can be treated as essentially frictionless.