HOT SHOTS BY THE NUMBERS
Kent Hannon's article An Idea That's Gotten Way Off the Ground (Nov. 28) on improved field-goal percentages in college basketball was read with great interest by the advanced placement physics class at Chats-worth ( Calif.) High School. His analysis of the phenomenal shooting of today's player was appreciated by all. Unfortunately, if a player starts with Professor Enoch Durbin's range formula, the result will be an "air ball." The proper expression is
r = Vo sin 2?/g
However, even the correct equation will give the range only if the ball takes off and lands at the same height and if there is no air resistance. Hence, the ball would have to be released at the height of the rim in a vacuum—a condition that would surely have a disastrous effect on spectator health. If the gym were not evacuated, other factors, such as the rotation of the ball, would have to be considered.
We do agree with Hannon that shooting a basketball is not something that can be reduced to a mathematical expression. If it were, the NBA would be stocked with Caltech grads.
ADVANCED PLACEMENT PHYSICS CLASS
Chatsworth High School
Professor Durbin's equation should read
R(range) = V(velocity)/G(gravity) sin2?
where ? is the angle from which the basketball is shot. This equation assumes that the ball is shot from the same height as the hoop, there is no air drag, the ball is not rotating, the ball is not banked off the glass or slam dunked.
This type of oversimplified analysis led some scientists to believe that a curve ball was an optical illusion.
Using your equation, the maximum range would be achieved by shooting the ball at a 90-degree angle (i.e., straight up). Better stick to sports!
BRADLEY S. DEHOFF
JEFFREY K. NATORI
JAMES S. SHOEMAKER
Alas, 2 sin ? does not equal sin 2 ?.
LAWRENCE K. HOYT
School of Engineering
New York City