The FIRST Robotics competition this year involved a basketball shooting robot. However, for various reasons, the basketball chosen for the competition was a "size 4" (grade-school size) basketball rather than a "size 7" (college/NBA) size basketball. The hoop/rim, however, was a standard 18" inner diameter rim with the center 15" from the backboard. I'm interested in what court dimensions would make this size 4 ball & standard size rim "equivalent" in difficulty with a standard size 7 ball and standard size rim. Here are the standard court dimensions: 15' from the free throw line to the projection of the backboard onto the floor; the top of the rim is exactly 10' from the floor. The standard size 7 basketball is 29.5-30" in circumference & weighs 22oz. --- The size 4 basketball has a circumference of 25" and a weight of 11.2oz. --- In order to make shooting a standard basket with a smaller/lighter ball "equivalent" in difficulty, how high above the floor should the rim be, and how far away from the free-throw line should the backboard be located? The tallest part of the robot may not exceed 84", so we can assume that the robots are shooting from approximately the same height as a tall adult human. --- My intuition is that air resistance may be negligible for this problem, but perhaps not.