Kinematics
Kinematics is represented all throughout ultimate frisbee. In ultimate frisbee, most of the game consists of throwing or passing as you can not run with the frisbee. Kinematics is defined as the study of the motion of objects using words, equations, graphs and diagrams and numbers. Kinematics is a study aimed at explaining the motion of objects (Physics Classroom,2014). During the game of ultimate frisbee, the frisbee is almost always in motion as you have to pass the frisbee to get it from one end of the field to another. Therefore kinematics is incorporated all throughout the game. For kinematics I will be focusing on the throwing of the frisbee as you can use kinematic equations to find the maximum height, acceleration and the maximum speed of a frisbee throw.
MAximum height
Shown below is the solutions needed to find the maximum height of a 0.72kg frisbee thrown at an angle of 30 degrees at a height of 0.911m with minimal air resistance.
These numbers make sense as the throw is a projectile. This means that the maximum height of the throw is in the middle of the pathway. As you can see from the picture the frisbee is not much higher than his head, so the angle degree he threw the frisbee at could not of been very large. The frisbee starts at a higher height then it finishes at so, to find the maximum height I needed to make sure I added the starting height from the height at the top of the projectile. I was able to find the maximum height after I calculated the horizontal velocity, vertical velocity and the resultant velocity by using equations I had learned in class. I knew from collecting my data that the frisbee had travelled 10.6m (which was measured by a meter stick) and that the time the frisbee was in the air was 1.66s (which was measured by a stopwatch). Therefore once collecting all of these numbers, I used one of the 'BIG FIVE' equations to calculate by maximum height. By doing this it allowed me to find the proper maximum height which was 1.6036m.
It is important for a frisbee player to understand how maximum height works and affects frisbees as in order to pass over a person with a tall reach they must understand that they need to throw it at a greater angle as it needs to reach a higher maximum height then throwing it over a person who is shorter. For example if a person that was 1.8288m was guarding you, verses someone that was 1.5240m. If you threw a frisbee at an angle of 30 degrees, and if they were standing right where the frisbee reached the maximum height they would be able to get it. Where as a person that was 1.5240m would have to reach or jump to try and interfere with the frisbees pathway. Therefore when wanting to through the frisbee at a higher maximum height you must increase the angle you throw the frisbee at.
It is important for a frisbee player to understand how maximum height works and affects frisbees as in order to pass over a person with a tall reach they must understand that they need to throw it at a greater angle as it needs to reach a higher maximum height then throwing it over a person who is shorter. For example if a person that was 1.8288m was guarding you, verses someone that was 1.5240m. If you threw a frisbee at an angle of 30 degrees, and if they were standing right where the frisbee reached the maximum height they would be able to get it. Where as a person that was 1.5240m would have to reach or jump to try and interfere with the frisbees pathway. Therefore when wanting to through the frisbee at a higher maximum height you must increase the angle you throw the frisbee at.
Acceleration
Shown below is the rate at which a 0.72kg frisbee accelerates, neglecting air resistance.
The frisbee’s pathway is a projectile. When an object is following a projectile pathway, only one force is acting on it and that is gravity. This means that the acceleration of the frisbee is 9.8m/s^2. The horizontal velocity stays the same throughout, meaning that there is no horizontal acceleration as there are no left or right forces acting on the object (Gibbs, 2013). The vertical velocity is slowing down as it reaches its maximum height due to gravity. As it starts to fall again after reaching maximum height it starts to speed up as gravity becomes stronger when you get closer to the certain of the earth. You also see above that the vertical velocity at the maximum height is zero. This is because at the peak itself, the velocity vector is entirely horizontal at this point in the trajectory (Physics Classroom, 2014).
Now if we were to look at the pathway of a frisbee with air resistance, it would not be seen the same as above. It would not look the same as above because we have two more forces acting on it. They are lift and drag. Lift was designed to make gravity have a harder time bring the frisbee down. This was done so the frisbee could have more of a float to it, so it could travel farther with less throwing force (Scodary,2007). Drag is the pull the wind has on the frisbee. When a frisbee is thrown it is being thrown into air, regardless of whether the wind is with the frisbee or against it there will always be some drag, but there will be a significantly more amount of drag when the frisbee is against the wind (Benson,2014). Lets say the frisbee was thrown with the wind, since it is not a projectile anymore because we've added two more forces the vertical and horizontal velocities would change throughout the throw because of these two forces. Below are equation of the vertical and horizontal accelerations at the start of the throw (when force is being applied):
Now if we were to look at the pathway of a frisbee with air resistance, it would not be seen the same as above. It would not look the same as above because we have two more forces acting on it. They are lift and drag. Lift was designed to make gravity have a harder time bring the frisbee down. This was done so the frisbee could have more of a float to it, so it could travel farther with less throwing force (Scodary,2007). Drag is the pull the wind has on the frisbee. When a frisbee is thrown it is being thrown into air, regardless of whether the wind is with the frisbee or against it there will always be some drag, but there will be a significantly more amount of drag when the frisbee is against the wind (Benson,2014). Lets say the frisbee was thrown with the wind, since it is not a projectile anymore because we've added two more forces the vertical and horizontal velocities would change throughout the throw because of these two forces. Below are equation of the vertical and horizontal accelerations at the start of the throw (when force is being applied):
After the frisbee leaves the person’s hand, it has no more force applied to it therefore the drag and lift will start to slow the frisbee down. The decreasing air speed is compensated for by the increasing of the lift coefficient. Drag reduces the forward velocity (horizontal velocity) and gravity (which exceeds lift) gives the frisbee a downward motion therefore the disc falls through the air at a steeper rate.
I was able to calculate the acceleration of the frisbee vertically and horizontally because of my previous equation calculations with finding maximum height and my data collected. I used one of the 'Big Five' equations to find my acceleration horizontally by adding in the distance it travelled (collected in data), the initial horizontal velocity (taken from maximum height equations) and the time it was in the air for (collected from data) into my equation. This gave me all the variables to punch into my equation to give me an answer of 5.472m/s^2. For my vertical acceleration I also used one of the 'Big Five' equations, this time punching into my equation the maximum height (found in the maximum height equations), the initial vertical velocity (taken from maximum height equations) and the time (collected from data). With these numbers I was able to find my vertical accelerating o 2.6831m/s^2 (down).
It is important for a frisbee player to understand acceleration when playing the game as it provides them with the advantage of knowing how much speed they need on their throw in order to reach a certain distance in a certain amount of time. It also does the opposite by allowing athletes to know how much acceleration their frisbee will have travelling a certain distance or time. It allows athletes to understand that the more force you apply to a mass the faster an object will accelerate (Newton’s second law).
I was able to calculate the acceleration of the frisbee vertically and horizontally because of my previous equation calculations with finding maximum height and my data collected. I used one of the 'Big Five' equations to find my acceleration horizontally by adding in the distance it travelled (collected in data), the initial horizontal velocity (taken from maximum height equations) and the time it was in the air for (collected from data) into my equation. This gave me all the variables to punch into my equation to give me an answer of 5.472m/s^2. For my vertical acceleration I also used one of the 'Big Five' equations, this time punching into my equation the maximum height (found in the maximum height equations), the initial vertical velocity (taken from maximum height equations) and the time (collected from data). With these numbers I was able to find my vertical accelerating o 2.6831m/s^2 (down).
It is important for a frisbee player to understand acceleration when playing the game as it provides them with the advantage of knowing how much speed they need on their throw in order to reach a certain distance in a certain amount of time. It also does the opposite by allowing athletes to know how much acceleration their frisbee will have travelling a certain distance or time. It allows athletes to understand that the more force you apply to a mass the faster an object will accelerate (Newton’s second law).
Maximum Speed
Shown below are equations for finding the maximum speed on a 0.72kg frisbee.
I was able to find my maximum speed of the frisbee as I already had the numbers needed, as I found them above. From there I used one of the 'Big Five' equations to calculate my maximum speed. I plugged in the vertical velocity (which was found when I solved for maximum height), the acceleration of gravity (always 9.8m/s^2) and the vertical height it travelled (also found when I solved maximum height). From there I was able to solve the equation and find out that the maximum speed of the frisbee thrown was 5.926m/s.
Maximum speed is the most amount of speed an object, in this case a frisbee, produces while in the air. Maximum speed is important for frisbee players to understand as they need to be able to throw the frisbees at different speeds to reach different lengths or cover a certain amount of metres in a certain period of time. The maximum speed on a frisbee will be right after the person lets go of the frisbee, this is because as the frisbee follows its parabola, the forces of lift and drag will start to affect the frisbee even more. Therefore when the frisbee is just released it has the least effects of drag and lift on it, resulting it in going it’s maximum speed then. They also must be aware of that gravity is always in affect every time an object is in the air. The distance the frisbee goes will also account for the speed of the frisbee as it will decipher how many metres per second the frisbee will fly.
Maximum speed is the most amount of speed an object, in this case a frisbee, produces while in the air. Maximum speed is important for frisbee players to understand as they need to be able to throw the frisbees at different speeds to reach different lengths or cover a certain amount of metres in a certain period of time. The maximum speed on a frisbee will be right after the person lets go of the frisbee, this is because as the frisbee follows its parabola, the forces of lift and drag will start to affect the frisbee even more. Therefore when the frisbee is just released it has the least effects of drag and lift on it, resulting it in going it’s maximum speed then. They also must be aware of that gravity is always in affect every time an object is in the air. The distance the frisbee goes will also account for the speed of the frisbee as it will decipher how many metres per second the frisbee will fly.