I was one of the estimated 111 million people to watch the Super Bowl last night. That's a lot of people watching a football game, though still an order of magnitude less than the number of people that watch the FIFA World Cup every four years. Still, the Super Bowl is the biggest game of the year in the US. It was a great game that came down to a Hail Mary from future Hall-of-Fame New England quarterback Tom Brady.
Like everyone else, I held my breath while the ball was in the air. I later analyzed the throw because I was curious how well Brady had thrown the pass. Watching the replay over and over, I averaged five timings of the ball's flight time and got 3.474 seconds. Brady appeared to let go of the ball at the New England 42-yard line; the ball was first touched about 6 yards deep in the end zone. That means that the horizontal range of the ball was about 64 yards (58.5 meters). Solving the equation of motion from Newton's second law, which includes air resistance, I found that Brady released the ball with a speed of 58.4 mph (94.0 km/hr) at an angle of about 45.3 degrees from the horizontal. The ball reached a maximum height of roughly 19.5 yards (17.8 meters) above the turf.
It was a great pass, and it needed a lot of luck to be completed. After being tipped, New England tight end Rob Gronkowski dove for the ball and looked to have a change to catch it. But, alas, even at 6' 6" (1.98 meters) tall, Gronkowski was too late getting to the ball. Once the ball was tipped, it began accelerating to the turf at 32 feet per second per second (9.8 meters per second per second), which is about 22 mph per second. Gronkowski simply had too much distance to cover while the ball was making its way to the turf and giving the Giants their fourth Super Bowl win.
See Chapter 3 of my book, which focuses on Doug Flutie's famous Boston College pass to beat Miami in 1984, for more details on modeling the flight of a Hail Mary pass in football.
"it began accelerating to the turf at 32 feet per second per second (9.8 meters per second per second), which is about 22 mph per second."
ReplyDeleteI believe you have one too many "per seconds" in there. Or I could be wrong.
Thanks for your comment. Acceleration units are indeed distance per time per time. What acceleration measures is the time rate of change of velocity; that's how we get velocity units over time units. Ignore air resistance and imagine dropping a ball from a five-story window. Each second of fall, the speed increases by 32 ft/s (or 22 mph). It takes just about a second for an object in free fall to reach the speed limit in a school zone!
DeleteWhat about Eli Manning's "Hail Mary" at the end of the first half of the NFC Divional game against the Packers? Or was the distance "too short" to truly be considered a Hail Mary pass?
ReplyDeleteGreat idea! I had not modeled that throw. Check out my latest blog post.
Deletecould you believe me if I tell you that I was one of the rest of the billions of people all around the world that did not watch the Super bowl?? I was going to watch it, but I got a call from my sportsbook software providers and I had to take care of the matter, but I watched the replay later, but I think it doesn't account to include me in the 111 million people, does it??
ReplyDelete