Growing up as a child in Asheboro, NC, I learned rather early that basic math—adding, subtracting, multiplication and division—all came very easily to me. Once I was able to master my multiplication tables to times 12, the World was my oyster when it came to nearly any basic math problem.
As a sports enthusiast, I relied on my imagination to come up with ways to employ math, to clarify certain sports concepts. Like most children, my creativity knew no bounds, so I kept an ongoing log of mental math problems going on in concert with sports. Many of these problems I did in my head. I had a math game for just about any sports issue one could name. The world of sports contained numbers galore, while the idea of quantifying certain aspects of it seemed to be ubiquitous in its sphere. There were all kinds of materials for me to pull from to gain better understanding of a specific sports phenomenon.
For some unknown reason, lately, the progress and evolution of sports, namely the ever-improving times in track and field events, has been occupying my mind. I guess one part of this is knowing that no matter how far down, over time, that humans push the World records to new lows, we all know that distances will require some time for completion. The theoretical and philosophical question, I always wonder about, is ,”How far down can we push those records? What are the absolute minimal amounts of time it will take to cover those distances?’ I can never really answer this question, but I feel it is the kind of question that is both imaginative and fun for a sports enthusiast.
Specifically, I wondered if math could help me to gain some idea of the distance gap that would occur between the current mens’ World record holder in the 100 meter dash and the winner at the 1988 Summer Olympic games in Seoul, Korea, if we could somehow pull the runners out-of-time and place them in the same race? The winner at the Seoul Olympics was Canadian Ben Johnson, who with a time of 9.79 seconds, was later disqualified for performance-enhancing drugs. The current world record holder is Usain Bolt of Jamaica, with a time of 9.58 seconds in Berlin in 2009. My question is simply, “How much distance would exist between Usain and Ben if they were in the same race, at the same time, and gave their best effort?”
In attempting to answer this question, there are a few details we must get out of the way first. Math can help us by giving us an average distance-covered-per-second for each runner, knowing that no human being runs the full 100 meters in a uniform-distance-per second over the entire race. For example, within the first ½ second or so to 2 seconds in, each runner is coming out of his sprinter’s crouch, with the desire to get upright and vertical as soon as possible. In this initial stage of the race, the runner is not moving with the same velocity as he will be, let’s say, at 50 meters into the race, when he is fully vertical and at the height of his explosion-and-full-flight speed. This means, for example that the runner will cover much more distance between the 4th and 6th seconds of the race than he did between the race’s beginning and the 2nd second. So, the best that math can do, is to give us each runner’s average-distance-per-second, as we remain careful to convert metric distances into the American standard of feet and inches, to help us clarify, and see, the actual finishing gap between the two runners.
A meter is equal to 39.37 inches, so we must multiply 39.37 times 100, to give us the total number of inches in 100 meters. The answer is 3,937 inches. Ben Johnson covered that distance in 9.79 seconds, so to find his distance-per-second speed, we need to divide the 3,937 inches of the race, by 9.79. The answer is 402.14505, which means that Ben’s average speed over the course of the race was 402.14505 inches per second. However, we know that Ben is going to lose the race, since Usain is running the distance in 9.58 seconds. So, how do we figure out (more or less?) where Ben is when Usain crosses the finish line? Well, we know Ben’s average distance-per-second, so all we have to do is figure out where Ben is when Usain crosses the line. Usain crosses the line at 9.58 seconds, so we multiply 9.58 times 402.1450 (Ben’s distance -per-second speed), to let us know. The answer is 3,852.5495 inches. The full race is 3, 937 inches. We take 3,937 (the full race) and subtract 3,852.5495, to find out where Ben is when Usain crosses the line. 3,937 minus 3,852.5495. The answer is 84.4505 inches. We know that there are 12 inches in 1 foot. We now divide 84.4505 by 12. The answer is 7.0375417. This means that Ben Johnson is a little more than 7 feet behind Usain Bolt, when Bolt finishes the 100 meter race, if both runners run their best time. Imagine and picture that distance inside of your head, which is quite substantial. Most world class sprinters defeat their nearest competitors by a step or two. Usain Bolt will beat Ben Johnson by more than 7 feet. For a sports nut, that is mind-blowing. And it has taken math to let us know this answer, which is just one indication of why math can be awesome, if one knows how to use it.
