How do Kinematics relate to Football?
Kinematics in general, is the study of mechanics which describes the motion of objects and systems without consideration of the causes of motion. Concepts of Kinematics can be seen and explored all over the football field, and are used to help explain the physics behind things such as the motion of a ball through the air, the acceleration and velocity of a running back in motion, a field goal being kicked, and much more. With footballs always soaring through the air, and running backs always scrambling and changing speeds throughout the field, kinematics is a huge factor when it comes to the sport of football.
Exploring Kinematics in Football
In order to further explore kinematics and the calculations behind it, we have brought our guest star “Sayf Al-Omaishi” from Bill Crothers Secondary School in to our studio to do some testing. We will first put his throwing arm up against one of the top NFL quarterbacks, and then we will see how his speed and acceleration compares to one of the NFL's fastest stars as well.
The Toss
Cam Newton
Cam Newton is one of the most versatile and respected quarterbacks in the NFL. He is known for being able to dance around in the pocket, and still deliver a deep powerful ball to his receivers when he finds the opening. In the NFL draft combine, prior to being drafted by the Carolina Panthers, Cam Newton preformed a quarterback ball velocity test where his most powerful throw would be measured by a radar gun. His throw was measured an outstanding 56 mph, which can be translated to 90 km/h, or 25 m/s. How can our guest Sayf Al-Omaishi compare? We will have to see.
Sayf Al-Omaishi
Unfortunately, there was no radar gun at our testing grounds when Sayf showed up for testing. What we did have though, was an elite group of physicists who would be able to calculate his throwing velocity, and max height, given simple measurements. During Sayf's test throw, he released the ball from about 1.5m from the ground, and we also made sure that the ball was also released at about a 30 degree angle from horizontal. The ball was caught at about 1.5m from the ground also, and our timers clocked in a time of 1.84 seconds for the 20m throw. He only threw 20m so the throw's velocity would stay almost constant throughout the throw, and not slow down much from release to catch.
Now let's see what the physics calculations are, behind this throw. The physicists will calculate the max height of the pass, and see how how Sayf's throwing velocity compares to
NFL star Cam Newton.
Now let's see what the physics calculations are, behind this throw. The physicists will calculate the max height of the pass, and see how how Sayf's throwing velocity compares to
NFL star Cam Newton.
Release Throwing Velocity
Time =1.84s
Horizontal Distance =20m
20/1.84 = 10.87m/s (Horizontal Velocity)
Vr cos30 = 10.87m/s
Vr = 10.87m/s / cos30
Vr = 12.55m/s
Sayf released the ball with a velocity of about
12.55m/s
Horizontal Distance =20m
20/1.84 = 10.87m/s (Horizontal Velocity)
Vr cos30 = 10.87m/s
Vr = 10.87m/s / cos30
Vr = 12.55m/s
Sayf released the ball with a velocity of about
12.55m/s
Max Height
Vvi = 12.55sin30
Vvi = 6.275m/s
a = -9.8m/s²
The Ball will reach max height when the Vertical Velocity is 0. (Vv=0)
Vvf² = Vvi² + 2ad
0 = (6.275)² + 2(-9.8m/s²)d
0 = 39.376 - 19.6d
-39.376 =-19.6d
-39.376/-19.6 = -19.6d/-19.6
d=2m + 1.5 m release height
d=3.5m
Sayf's throw reaches a max height of about 3.5m.
Vvi = 6.275m/s
a = -9.8m/s²
The Ball will reach max height when the Vertical Velocity is 0. (Vv=0)
Vvf² = Vvi² + 2ad
0 = (6.275)² + 2(-9.8m/s²)d
0 = 39.376 - 19.6d
-39.376 =-19.6d
-39.376/-19.6 = -19.6d/-19.6
d=2m + 1.5 m release height
d=3.5m
Sayf's throw reaches a max height of about 3.5m.
Verdict
The calculations are in, and we can now clearly see that these two are incomparable... As we said earlier, Cam Newton's throwing velocity test showed that he releases the ball with a velocity of about 25m/s. How did our guest Sayf Al-Omaishi do? Sayf's throw measured a release velocity of 12.55m/s, just over half as powerful as Cam's throw. Our professionals have come to the conclusion that you do not want Sayf behind the line on your football team, and that he desperately needs to work on his arm...
The Run
Chris Johnson
When talking about the run in the NFL, go no further than Chris Johnson. Chris Johnson is one of the most electrifying players in the NFL, with his pure explosiveness and speed. He has made the pro bowl as a starter in each of his first 3 seasons in the NFL, which has helped him establish himself as one of the elite running backs in the league today. He holds the record for the fastest 40 yard dash time in NFL combine history, with a time of 4.24 seconds. Does our guest star Sayf Al-Omaishi have a chance at matching this? Definitely not, but we will see how he measures up in max speed and acceleration...
Average Speed Sayf Al-Omaishi
On our testing grounds, Sayf ran 40 metres in 5.53 seconds. Chris Johnson on the other hand, ran 40 yards (36.57m) in 4.24s. Let's see what average velocity that gives them, so we can find out their max speeds and calculate acceleration.
Sayf: Chris Johnson:
Vav = d/t Vav = d/t
Vav = 40m/5.53s Vav = 36.57m/4.24s
Vav = 7.23m/s Vav = 8.63m/s
Sayf: Chris Johnson:
Vav = d/t Vav = d/t
Vav = 40m/5.53s Vav = 36.57m/4.24s
Vav = 7.23m/s Vav = 8.63m/s
Acceleration
(Our professionals predict it takes our athletes 3.5 seconds
to reach max speed in their sprints, and they no longer
accelerate after 3.5 s. That number will be put in for time to
find the accelerations and Max speeds of both athletes.)
Sayf: Chris Johnson:
Vav = 7.23m/s Vav = 8.63m/s
Vi = 0m/s Vi = 0m/s
Vf = ? Vf = ?
Vav = (Vi + Vf) / 2 Vav = (Vi + Vf) / 2
Vf = 2Vav - Vi Vf = 2Vav - Vi
Vf = 2(7.23m/s) - 0 Vf = 2(8.63m/s) - 0
*Vf = 14.46m/s *Vf = 17.26m/s
a = (Vf - Vi) / T a = (Vf - Vi) / T
a = (14.46m/s - 0) / 5.53s a = (17.26m/s - 0) / 4.24s
a = 2.61m/s² a = 4.07m/s²
Sayf's acceleration is 2.61 m/s² for 3.5 Chris Johnson's acceleration is 4.07 m/s² for 3.5
seconds until he reaches max speed. seconds until he reaches max speed.
* - This is not the actual max speed. Look below.
to reach max speed in their sprints, and they no longer
accelerate after 3.5 s. That number will be put in for time to
find the accelerations and Max speeds of both athletes.)
Sayf: Chris Johnson:
Vav = 7.23m/s Vav = 8.63m/s
Vi = 0m/s Vi = 0m/s
Vf = ? Vf = ?
Vav = (Vi + Vf) / 2 Vav = (Vi + Vf) / 2
Vf = 2Vav - Vi Vf = 2Vav - Vi
Vf = 2(7.23m/s) - 0 Vf = 2(8.63m/s) - 0
*Vf = 14.46m/s *Vf = 17.26m/s
a = (Vf - Vi) / T a = (Vf - Vi) / T
a = (14.46m/s - 0) / 5.53s a = (17.26m/s - 0) / 4.24s
a = 2.61m/s² a = 4.07m/s²
Sayf's acceleration is 2.61 m/s² for 3.5 Chris Johnson's acceleration is 4.07 m/s² for 3.5
seconds until he reaches max speed. seconds until he reaches max speed.
* - This is not the actual max speed. Look below.
Max Speed
To find max speed, we will just need to plug in the acceleration we have found, and the time for which the athletes accelerate. Since the initial velocity is 0, it will not have an affect.
T (until done accelerating) = 3s T (until done accelerating) = 3s
Vf = a x t + Vi Vf = a x t + Vi
Vf = (2.61m/s²) x (3.5s) Vf = (4.07m/s²) x (3.5s)
Vf = 9.14m/s Vf = 14.24m/s
Sayf reaches a max speed of 9.14m/s Chris Johnson reaches a max speed of 14.24m/s
T (until done accelerating) = 3s T (until done accelerating) = 3s
Vf = a x t + Vi Vf = a x t + Vi
Vf = (2.61m/s²) x (3.5s) Vf = (4.07m/s²) x (3.5s)
Vf = 9.14m/s Vf = 14.24m/s
Sayf reaches a max speed of 9.14m/s Chris Johnson reaches a max speed of 14.24m/s
Verdict
After calculating Sayf and Chris Johnson's accelerations and max speeds throughout their runs, our prediction has been confirmed and Sayf was once again blown out. Sayf's speed and acceleration was no match for one of the NFL's greatest and fastest stars. Chris Johnson's outstanding 4.07 m/s² acceleration left Sayf in his dust, and reaching a max speed more than 50% larger than Sayf's, really showed the fans who's boss.