Gridiron physics: Scalars and vectors - Michelle Buchanan

Transcriber: Andrea McDonough
Reviewer: Bedirhan Cinar

Fourth and nineteen, folks, they've gotta have a play as time's ticking away because they've got to stay in this ball game, they've got to win. They come out lined up in the empty set, three receivers to the right, two to the left. Defense looks like they're gonna to man up with no safety. This is the exact offensive match-up that they want: the best receiver lined up against the linebacker.

Quarterback steps back to receive the ball, five yards deep in the gun. He takes a snap, drops three steps, he plants his back foot, he's looking for an opening. There's a blitz coming off the edge! He steps up to avoid the rush. He's looking down field. He's got the inside receiver making a cut. He's got a step on the linebacker. Quarterback has a beat on it. He lets the ball go, it's in the air! Receiver is out in front of the defender. He's got it beat! He's out in front, racing for the ball! It's coming down! He cradles it at the fifteen! He's at the ten, five! Touchdown! Unbelievable play!

Now, wait a minute. Of course, it's believable, it's physics, specifically the differences between scalars and vectors. So, let's just see that replay. "Quarterback steps back to receive the ball, five yards deep in the gun." Stop. See, measurements are defined as two different quantities. Scalars are measurements with only numbers, and vectors are measurements with direction.

For example, when that quarterback takes the snap, he's five yards away, but from where? Back from the line of scrimmage, so the five yards by itself is a scalar quantity. When you add a direction, like five yards deep, it becomes a vector quantity. Five yards - scalar, five yards deep - vector. OK, go ahead. "He takes a snap, drops three steps. He plants his back foot, he's looking for an opening. There's a blitz coming off the edge! He steps up to avoid the rush."

Whoa! Here's a difference between distance and displacement. Distance is a measurement without identifying where you moved. It's a scalar quantity. When the quarterback makes a three-step drop, he moves about three yards back. When he moves about another three yards forward, when he steps up into the pocket, so that quarterback moves a total distance of six yards. That's a distance, that's a scalar.

Now, displacement is a vector quantity, describing about how far out of place the object is. So the quarterback dropped back three yards and then moved back forward three yards, he's in the exact same place where he started. So, his displacement is zero yards. Distance - six yards, displacement - zero yards.

So, let's look at what happened next. "Quarterback has a beat on it, he lets the ball go! It's in the air! Receiver is out in front of the defender." Stop. So, here's speed and velocity, but let's just do one thing at a time. So, speed is measurement without direction, it's a scalar quantity. Velocity is a vector quantity. It is that object's speed, but with a direction of motion.

So the receiver accelerates away, gaining both speed and distance. This takes the receiver 5 seconds to run those 50 yards. So his average speed, in any given time, is 10 yards/second. The linebacker tries to keep up, but his overall speed is slower, he only goes 35 yards in those 5 seconds, so his average speed is only 7 yards/second. They're both traveling in a forward direction, so their velocity is also positive.

You can't go from resting to your peak speed immediately. You've got to build up to it. This is acceleration. At first the linebacker can keep up with that receiver, but eventually the faster receiver pulls away. That's acceleration, the change in speed over time. Acceleration is a vector quantity. It describes a rate at which an object changes velocity. Like velocity, acceleration is a vector. It happens in a direction.

So let's just look at that play just one more time. "Quarterback steps back to receive the ball, five yards deep in the gun." Vector! "He takes a snap, drops three steps, he plants his back foot. He's looking for an opening. There's a blitz coming off the edge! He steps up to avoid the rush." Displacement! "He's got the inside receiver making a cut. He's got a step on the linebacker. The quarterback has a beat on it. He lets the ball go! It's in the air! Receiver is out in front of the defender!" Velocity!

"He's got it beat! He's out in front, racing for the ball! It's coming down! He cradles it at the fifteen, he's at the ten, five!" Acceleration! "Touchdown! Unbelievable play! That was a great play as time expired, resulting in the touchdown and ultimately the win and pure effort." And pure science.