NBC's Lester Holt looks at the role vectors play every time an NFL quarterback throws a pass. With the help of former NFL quarterback Joey Harrington, NSF-funded scientist John Ziegert of Clemson University and NSF-funded mathematician Rhonda Hughes of Bryn Mawr College explain how to use vectors to calculate the speed and direction needed for a completed pass. "Science of NFL Football" is a 10-part video series funded by the National Science Foundation and produced in partnership with the National Football League.
Science of NFL Football - Vectors
LESTER HOLT, reporting:
One of the most spectacular plays in NFL football is when a quarterback throws the ball right into the hands of his receiver with a pass so fast and accurate, it's called "threading the needle".
JOEY HARRINGTON (Former NFL Quarterback): It means putting a ball in a window that is so tight that only, you know, only that football could-- could fit through there…
HOLT: The speed and direction the football needs to reach a receiver is a great example of what's known in math and science as a "vector" - because it has both a length and a direction. In this case, it's a velocity vector.
Dr. JOHN ZIEGERT (Clemson University): The quarterback has under his control how hard he throws the ball or with what speed and in what direction.
HOLT: To understand the role velocity vectors play in an NFL pass, we filmed former NFL quarterback Joey Harrington, who played for the Detroit Lions and most recently with the New Orleans Saints, using a special high-speed camera called a Phantom Cam.
Offscreen Voice: Stand by and action Joey.
HOLT: On the receiving end is Antonio Freeman, former wide receiver with the Green Bay Packers.
ANTONIO FREEMAN (Former NFL Wide Receiver): It's like playing Monday night with the bright lights.
HOLT: The moment the football leaves Harrington's hand, it has velocity - both a direction and a speed. On average, an NFL quarterback can throw between 45 to 50 miles per hour. It's possible to represent the ball's velocity vector with an arrow.
While this vector is easy to draw for a pass from a stationary quarterback, rarely does a quarterback have the luxury of just standing and throwing. Oftentimes, he gets flushed out of the pocket, creating a whole a new vector - his own velocity vector.
Dr. RHONDA HUGHES (Bryn Mawr College): The target is where he wants the ball to go, so he has to understand that if he's running, he's going to throw the ball in another direction.
HOLT: It's possible to add these two vectors together to find a third vector - the actual velocity the ball needs to reach the receiver. This vector can be found using the so-called "parallelogram method" for adding vectors.
Dr. HUGHES: We take our two vectors, and we form a parallelogram, which is a four-sided object, with opposite sides parallel.
HOLT: Using the parallelogram's geometry, the vector sum is determined.
Dr. HUGHES: So, we take our parallelogram, and the sum of these two vectors is simply the diagonal of the parallelogram.
HOLT: …Which makes it all the more important that the receiver is at the right place at just the right time to receive the pass.
FREEMAN: So you as a receiver have to know what your job is, where you're supposed to be on a football field, to have the ball thrown to you, you never know how fast a defense is going to react to which receiver and which one is going to be open. So you have to run each route, as if you're getting the ball.
HOLT: Making the quarterback's skills all the more impressive. In a real game, he must calculate all of these vectors in a split second: the vector of his rollout, the vector of the receiver, and the vector the ball must fly to reach its target.
HARRINGTON: It's a really good feeling when you put that ball exactly where it needs to be…
HOLT: And for an NFL quarterback, that means safely in the hands of his receiver.
Math & Statistics Activities:
Draw a square, a rectangle and a parallelogram.
Draw three different parallelograms.
A box score is more than a capsule archive. It is a precisely etched miniature of the sport itself, for baseball, in spite of its grassy spaciousness and apparent unpredictability, is the most intensely and satisfyingly mathematical of all our outdoor sports.” — Roger Angell, The New Yorker
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