Kinematics:
Cam Newton of the Carolina Panthers
Kinematics: Is the branch of physics that analyzes motion in terms of time and distance.
In football one of the most important components is being able to throw or kick a football, more importantly to throw or kick a football in order to score. One way of doing this is to throw or kick a football with a high velocity/speed. One of the best quarterback's in the NFL right now is the newcomer, Cam Newton who plays for the Carolina Panthers. He is a key example of a quarterback who has high velocity/speed on a football throw. For our example, Cam throws a football for 20 yards which is 18.288 metres and it took 1.25 seconds to reach the wide receiver. To figure out the speed of the football we can use the formula for speed which is: v = d/t (where 'v' represents the speed/velocity, 'd' represents the distance and 't' represents the time taken). So in this example v = 18.288m/1.25s, v = 14.6304m/s or if we use significant digits the answer would be 14.6m/s or 52.6km/hr. If we increase the distance to a hail mary which could be 50 yards (45.72 metres) the time taken will also increase, but since the path of the football will have a projectile motion the arc will also increase. The time taken for the football to reach the wide receiver is 2.75 seconds. The speed is: v = d/t, v = 45.72m/2.75s, the speed is v = 16.6255m/s and if we use significant digits, the answer would be 16.6m/s or 59.8km/hr. Speed is scalar because it is just a measurement. Velocity is vector so it is the same as speed except it has a direction. The direction will always depend on if the football is thrown or kicked directly up the field or to the right or left. Acceleration is the change in speed of an object over a certain time. To find out the acceleration of the football thrown from 20 yards (18.288 metres) to 50 yards (45.72 metres) we will use the formula a (acceleration) = v2 (second speed) - v1 (first speed)/t2 (second time) - t1 (first time). We will use the speed and time from the first example as well. The acceleration is: a = 16.6255 - 14.6304/2.75 - 1.25, a = 1.9951/1.50, a = 1.3301m/s squared and if we use significant digits, the answer would be 1.3m/s squared. Therefore the football accelerated for 1.3301m/s squared between 20 yards and 50 yards. By knowing this quarterbacks will know how fast they are throwing the football, so they would know to either work on their technique or strength in order to increase the speed of the football and perform at a higher level.
In football one of the most important components is being able to throw or kick a football, more importantly to throw or kick a football in order to score. One way of doing this is to throw or kick a football with a high velocity/speed. One of the best quarterback's in the NFL right now is the newcomer, Cam Newton who plays for the Carolina Panthers. He is a key example of a quarterback who has high velocity/speed on a football throw. For our example, Cam throws a football for 20 yards which is 18.288 metres and it took 1.25 seconds to reach the wide receiver. To figure out the speed of the football we can use the formula for speed which is: v = d/t (where 'v' represents the speed/velocity, 'd' represents the distance and 't' represents the time taken). So in this example v = 18.288m/1.25s, v = 14.6304m/s or if we use significant digits the answer would be 14.6m/s or 52.6km/hr. If we increase the distance to a hail mary which could be 50 yards (45.72 metres) the time taken will also increase, but since the path of the football will have a projectile motion the arc will also increase. The time taken for the football to reach the wide receiver is 2.75 seconds. The speed is: v = d/t, v = 45.72m/2.75s, the speed is v = 16.6255m/s and if we use significant digits, the answer would be 16.6m/s or 59.8km/hr. Speed is scalar because it is just a measurement. Velocity is vector so it is the same as speed except it has a direction. The direction will always depend on if the football is thrown or kicked directly up the field or to the right or left. Acceleration is the change in speed of an object over a certain time. To find out the acceleration of the football thrown from 20 yards (18.288 metres) to 50 yards (45.72 metres) we will use the formula a (acceleration) = v2 (second speed) - v1 (first speed)/t2 (second time) - t1 (first time). We will use the speed and time from the first example as well. The acceleration is: a = 16.6255 - 14.6304/2.75 - 1.25, a = 1.9951/1.50, a = 1.3301m/s squared and if we use significant digits, the answer would be 1.3m/s squared. Therefore the football accelerated for 1.3301m/s squared between 20 yards and 50 yards. By knowing this quarterbacks will know how fast they are throwing the football, so they would know to either work on their technique or strength in order to increase the speed of the football and perform at a higher level.
Vector's
Football Vectors
When a quarterback is being ambushed by the defence, he has to move while holding onto the football. Once he passes the football to the wide receiver, the ball is caught vertically above the quarterback, but the wider receiver will up being vertically above where the quarterback was before, thus creating a parallelogram. The ball initially travels from the starting point to where the wide receiver catches it. If this line is drawn it creates two triangles in the parallelogram. Then we would have to find out the resultant displacement, which is the total distance the football travels from point A to point B. This can help an athlete in football, specifically a quarterback, because he will know when the defence is ambushing him and at which angle and time to throw the football in order to complete the play effectively.
Projectile Motion:
Cam Newton of the Carolina Panthers
If Cam Newton throws a football over a long distance such as a hail mary, or is kicked, the motion the football travels in is a parabolic motion. Since there is air resistance, the ball will start to decelerate before it reaches the max height of the throw, and will begin to fall back down to the ground as gravity will take into effect. The average height of a quarterback in the NFL (National Football League) is six feet. If the ball is thrown for 50 yards which is 45.72 metres to the wide receiver (whose average height is six feet which is 1.8288 metres) at a total speed of 16.6255m/s which we will say is 10.31275m/s vertically and 6.31275m/s horizontally and is released at a 59 degree, we can calculate the max height in which the football will reach. We also know the time taken is 2.75 seconds and the acceleration is 1.3301m/s squared. To do so we will organize the variable into two categories, vertical and horizontal.
Vertical:v1v = 10.31275m/s
av = -9.8m/s squared (acceleration of gravity) dv = 1.8288m t = 2.75s dvmax = ? v vertical max = ? | Horizontal:v1h = v2h = 6.31275m/s
ah = 1.3301m/s squared dh = 45.72m t = 2.75s |
We also know that the speed at the max height will be zero because it has stopped moving upwards, but hasn't started to move downwards so therefore the football has stopped in mid-air. We can now use the formula v2 squared = v1 squared + 2ad to solve for the maximum height. We will use the variables from the vertical column since the maximum height falls into the vertical category. The maximum height is: 0 ^ 2 = 10.31275^ 2 + 2(-9.8)dv, 0 = 102.5663 + -19.6dv, -102.5663 = -19.6dv, -102.5663/-19.6 = dv, dv = 5.2330m and if we use significant digits the answer would be 5.23m. We now have to add this value to the height of the quarterback since the ball is being released at the top of a quarterback's reach. If the quarterback has a standing reach of 2.4384m and we had 5.2330m to this value the max height in which this football will reach is 7.6714m. This will help quarterbacks know at what angle, or arm strength to throw the ball in order to complete a long pass effectively.
Science of NFL Football: Kinematics: http://science360.gov/obj/video/844d3b8f-5fe2-4907-928c-70f83023bd5c
Science of NFL Football: Projectile Motion and Parabolas: http://science360.gov/obj/tkn-video/fc729ef0-22ee-4f61-bb2a-b6c07685fb02
Science of NFL Football: Vectors: http://science360.gov/obj/tkn-video/0ca015f8-0d4c-4d0b-a31e-257ba1445c32
Science of NFL Football: Projectile Motion and Parabolas: http://science360.gov/obj/tkn-video/fc729ef0-22ee-4f61-bb2a-b6c07685fb02
Science of NFL Football: Vectors: http://science360.gov/obj/tkn-video/0ca015f8-0d4c-4d0b-a31e-257ba1445c32