NBC's Lester Holt looks at the science of projectile motion and parabolas with the help of former NFL punter Craig Hentrich. NSF-funded scientists Jim Gates from the University of Maryland and John Ziegert of Clemson University, and NSF-funded mathematician Rhonda Hughes from Bryn Mawr College, explain the significance of vertical and horizontal velocity on the trajectory every time an NFL punter kicks a football into the sky. "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 - Projectile Motion & Parabolas
LESTER HOLT, reporting:
With more than a thousand punts over a 16-year NFL career, Craig Hentrich knows down to his toes the secrets of a perfect punt.
CRAIG HENTRICH (Former NFL Punter): When you make contact with that ball it's almost a feeling that you don't fell the ball on your foot. It's almost like you're swinging your leg in air, when the ball comes off there perfectly.
HOLT: Elite kickers like Hentrich have been known to launch a football 120 feet in the air at speeds of up to 90 miles per hour. These powerful punts are a perfect example of projectile motion. And the arc the ball makes as it slices through the air is something that has been studied by scientists for centuries...all the way back to Galileo Galilei, one of the great thinkers of the Renaissance.
Dr. JIM GATES (University of Maryland): He's one of the first people in western science to realize that the shape of that curve is something the mathematicians had been talking about for a couple thousands years, it's called a parabola.
HOLT: To help us understand projectile motion and parabolas, we asked Hentrich to perform his craft in front of a super high-speed camera, called a Phantom Cam. It all begins with "the drop".
HENTRICH: The ideal drop, the ball has to stay level or with the nose or the front of the ball slightly up. At the moment of impact to the ball our leg will actually snap and actually straight now at that moment and that's the exact moment that you want to make contact with the ball.
HOLT: And up it goes...following a path...and the laws of gravity.
Dr. RHONDA HUGHES (Bryn Mawr College): Once a punter kicks a football, it becomes what we call a projectile. And it follows a path that we would also call a parabolic arc, or a parabola.
HOLT: As the football flies through the air in the shape of a parabola, there are two main components of velocity affecting the ball.
Dr. JOHN ZIEGERT (Clemson University): It has a horizontal component, the speed it's traveling along the ground, and a vertical component, the speed it's moving vertically.
HOLT: These two velocity components, the vertical and the horizontal, can be represented as "vectors".
Dr. HUGHES: A vector is basically an arrow in two dimensions that describes some kind of physical quantity.
HOLT: In this case, vectors show the physical quantities of speed and direction. The greater the speed, the longer the velocity vector. As gravity tries to slow the ball down, the vertical velocity vector gets smaller.
Dr. HUGHES: Gravity is acting on it from the instant that it leaves the player's foot. and-- but the effect of gravity is-- is demonstrated by the fact that the speed of the ball is decreasing.
HOLT: Gravity eventually causes the football to stop rising and reach the top point of its trajectory.
Dr. GATES: When it's at the high point, something very curious goes on. It has no up and down speed at all. So the up and down speed of a ball at its maximum point of arch is zero.
HENTRICH: Our goal in punting is to get the ball to hang or-- hang in the air to be in the air as long as possible.
Dr. GATES: And then it begins to come down, and the speed goes from zero, and then it comes back down really fast.
HOLT: Gravity pulls the ball back down to earth. As it gains more speed, the vertical velocity vector, now points downward.
Dr. ZIEGERT: When it starts to come back down to the ground, the vertical component of velocity is in the opposite direction, and the horizontal component is still the same.
HOLT: And down it goes until...it reaches its mark.
HENTRICH: There was always a great feeling to get as a punter to watch that ball going in the air knowing that you would hit it perfectly.
HOLT: Parabolas come in all shapes and sizes, but it takes NFL punters like Craig Hentrich to turn science into an art form.
Math & Statistics Activities:
Draw a parabola, or a parabolic arc.
Find examples of parabolas in photographs or drawings of buildings, bridges and other structures.
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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