The Task
My group, Ash, Daniel, and I, was assigned the task to create a video explaining the physics of a sports movement. We decided to study the physics of a basketball free throw. Our final numbers were to find the total velocity of the ball, the angle of the free throw, and the force applied on the ball.
The Process
We began the project by creating the motherboard. Early on we had minor disagreements on how to create it, but we all eventually consented. There would be 2 boards: the first was with the general idea for each part of the video, and the second was more specific, expanding each major block by explaining each individual scene. After developing the motherboard, we created the script. The following is the script:
"Derek: Hello everyone, my name is Derek,
Daniel: I’m Daniel,
Ashley: and I’m Ashley,
Derek: And welcome to our explanation for the physics of a free throw!
Daniel: On a foul committed by the defense, if the team committing the foul is in the penalty situation or the fouled player was in the act of shooting, the fouled player is awarded free throws.
Derek: Here, you see Daniel shooting a proper free throw.
Daniel: Start off at the free throw line with your feet parallel to the hoop having your dominant foot slightly ahead with both feet tilted. Some players like a bigger tilt, while some others like a smaller one. Bring the ball up with your dominant hand underneath ball and nondominant on the side to support the motion of bringing the ball up to your setpoint. Have ball loaded at 90 degree angle and release your shot with a flick of the wrist releasing the ball towards the rim, all while bending your knees correspondingly with your shot, releasing ball as knees extend in jumping motion without leaving the ground.
Derek: Okay, so a basketball has a mass of 0.625 kg. This is about 1.4 pounds. The freethrow line is 15 ft away from the hoop and the height of the hoop is 10 ft. Daniel is 150 pounds and 6 ft tall. Daniel wants to make sure the ball travels in an arc, so he needs to throw the ball about 10.5 ft high and 15 ft far.
Ashley: When the ball is thrown, since it travels in an arc, it takes 0.78s to reach its top height. We can now find the velocities of the ball. These can be found by dividing distance by time. The ball travels at 4.6 m/s horizontally, and 7.6 m/s vertically. We can now use the Pythagorean Theorem to find the total velocity of the ball. This is about 8.9 m/s, or about 20 mph. SInce we are given the 3 side lengths, we can find the angle the ball is thrown at. This is about 59 degrees.
Derek: Now that we have the total velocity, we can find the momentum of the ball. We do this by multiplying mass, 0.625 kg, by total velocity, 8.9 m/s, to get a momentum of about 5.6 Ns. Impulse always equals momentum, so impulse is also 5.6 Ns. With impulse, we can find the force applied on the ball. We figured out that Daniel applies force on the ball for about 0.26s. So, we can divide impulse by the time the force is applied to find the force. This is 22 N, or about 5 pounds.
Ashley: In short, to perform a successful free throw, throwing the ball at a 59 degree angle with about 5 pounds of force works. Of course, these numbers vary from person to person, since height affects the needed force and angle. However, for the average 6ft person, these numbers work excellently.
Derek: Thank you for listening to our video! We hope you’ve enjoyed our work!
Daniel: And now, disco!"
After writing the script, we began developing the film. I made the calculations and then put the numbers into the script. Ash filmed many scenes and began stringing them together. We did voice overs for the audio. After all the filming and recording was finished, Ash began editing the film. After a couple weeks of hard work, we successfully created our first video. This is it:
"Derek: Hello everyone, my name is Derek,
Daniel: I’m Daniel,
Ashley: and I’m Ashley,
Derek: And welcome to our explanation for the physics of a free throw!
Daniel: On a foul committed by the defense, if the team committing the foul is in the penalty situation or the fouled player was in the act of shooting, the fouled player is awarded free throws.
Derek: Here, you see Daniel shooting a proper free throw.
Daniel: Start off at the free throw line with your feet parallel to the hoop having your dominant foot slightly ahead with both feet tilted. Some players like a bigger tilt, while some others like a smaller one. Bring the ball up with your dominant hand underneath ball and nondominant on the side to support the motion of bringing the ball up to your setpoint. Have ball loaded at 90 degree angle and release your shot with a flick of the wrist releasing the ball towards the rim, all while bending your knees correspondingly with your shot, releasing ball as knees extend in jumping motion without leaving the ground.
Derek: Okay, so a basketball has a mass of 0.625 kg. This is about 1.4 pounds. The freethrow line is 15 ft away from the hoop and the height of the hoop is 10 ft. Daniel is 150 pounds and 6 ft tall. Daniel wants to make sure the ball travels in an arc, so he needs to throw the ball about 10.5 ft high and 15 ft far.
Ashley: When the ball is thrown, since it travels in an arc, it takes 0.78s to reach its top height. We can now find the velocities of the ball. These can be found by dividing distance by time. The ball travels at 4.6 m/s horizontally, and 7.6 m/s vertically. We can now use the Pythagorean Theorem to find the total velocity of the ball. This is about 8.9 m/s, or about 20 mph. SInce we are given the 3 side lengths, we can find the angle the ball is thrown at. This is about 59 degrees.
Derek: Now that we have the total velocity, we can find the momentum of the ball. We do this by multiplying mass, 0.625 kg, by total velocity, 8.9 m/s, to get a momentum of about 5.6 Ns. Impulse always equals momentum, so impulse is also 5.6 Ns. With impulse, we can find the force applied on the ball. We figured out that Daniel applies force on the ball for about 0.26s. So, we can divide impulse by the time the force is applied to find the force. This is 22 N, or about 5 pounds.
Ashley: In short, to perform a successful free throw, throwing the ball at a 59 degree angle with about 5 pounds of force works. Of course, these numbers vary from person to person, since height affects the needed force and angle. However, for the average 6ft person, these numbers work excellently.
Derek: Thank you for listening to our video! We hope you’ve enjoyed our work!
Daniel: And now, disco!"
After writing the script, we began developing the film. I made the calculations and then put the numbers into the script. Ash filmed many scenes and began stringing them together. We did voice overs for the audio. After all the filming and recording was finished, Ash began editing the film. After a couple weeks of hard work, we successfully created our first video. This is it:
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We showed it to the class and got some feedback. As we fixed and tweaked the video, we discovered a major error in my calculations! We forgot to take into consideration that the free throw was in an arc, not a triangle. We had to quickly recalculate the numbers, and successfully pulled it off and rerecorded the changed parts in the last day.
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The Final ProductThe video is approximately 3 minutes long. Our first part introduces us and explains what a free throw is. Then, the rest of the video explains the physics of the free throw, figuring out the total velocity of the ball, the angle of the free throw, and the force applied on the ball.
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Major Physics Concepts Used in the Project
Momentum (p) - This is the quantity of motion in a moving object. This is found by multiplying mass (m) by velocity (v). The unit is newton seconds (Ns).
Example - When the ball is thrown, it has a momentum of about 5.6 Ns.
Force of Impact - This is how hard something hits upon smashing into something else. This is found by dividing momentum by the time the force is applied. The unit is newtons (N).
Example - Daniel applies about 22 N of force onto the ball. This means he pushed with a force of about 5 pounds.
Impulse (J) - Impulse is the change in momentum. This is calculated by multiplying the force applied onto the object (F) to the time the force was applied (t). The unit is newton seconds (Ns).
Example - The ball goes from 0 Ns to 5.6 Ns, meaning that the change in momentum, or impulse, is also 5.6 Ns.
Vertical Velocity - This is how fast an object is moving vertically. However, to find vertical velocity, rather than dividing distance by time, we must multiply acceleration due to gravity (g) by time (t) because vertical velocity is not constant. The unit is meters per second (m/s).
Example - When thrown, the ball travels at a vertical velocity of 7.6 m/s.
Horizontal Velocity - This is how fast an object is moving horizontally. Horizontal velocity is not affected by vertical velocity, so the equation to find horizontal velocity is to just divide distance (d) by time (t). The unit is meters per second (m/s).
Example - When thrown, the ball travels at a horizontal velocity of 4.6 m/s.
Total Velocity - If we are the given the vertical and horizontal velocity of a moving projectile, we can find it's total velocity by using the Pythagorean Theorem (a^2 + b^2 = c^2). The velocities form a right triangle. The vertical and horizontal velocities are the legs and the total velocity is the hypotenuse. We can use the Pythagorean Theorem to find the hypotenuse, or in this case, the total velocity.
Example - If we square and add 7.6 m/s and 4.6 m/s we get 79.21 m/s, and square rooting that gives us a total velocity of 8.9 m/s.
d=1/2at^2 - This equation is used to find the distance an object travels when it's not moving at a constant velocity. This means that we use this equation to find vertical distance since vertical velocity is affected by acceleration due to gravity (g).
Example - Using this equation
Tangent - This is a trigonometric function used to find the angle measure of one of the angles in a triangle. This is found by dividing the opposite side by the adjacent side, then converting it into degrees by using an arctangent.
Example - To find tangent, we divide 7.6 m/s by 4.6 m/s. This is 1.65, and the arctangent of this number is about 59 degrees. This is the angle of the free throw.
Example - When the ball is thrown, it has a momentum of about 5.6 Ns.
Force of Impact - This is how hard something hits upon smashing into something else. This is found by dividing momentum by the time the force is applied. The unit is newtons (N).
Example - Daniel applies about 22 N of force onto the ball. This means he pushed with a force of about 5 pounds.
Impulse (J) - Impulse is the change in momentum. This is calculated by multiplying the force applied onto the object (F) to the time the force was applied (t). The unit is newton seconds (Ns).
Example - The ball goes from 0 Ns to 5.6 Ns, meaning that the change in momentum, or impulse, is also 5.6 Ns.
Vertical Velocity - This is how fast an object is moving vertically. However, to find vertical velocity, rather than dividing distance by time, we must multiply acceleration due to gravity (g) by time (t) because vertical velocity is not constant. The unit is meters per second (m/s).
Example - When thrown, the ball travels at a vertical velocity of 7.6 m/s.
Horizontal Velocity - This is how fast an object is moving horizontally. Horizontal velocity is not affected by vertical velocity, so the equation to find horizontal velocity is to just divide distance (d) by time (t). The unit is meters per second (m/s).
Example - When thrown, the ball travels at a horizontal velocity of 4.6 m/s.
Total Velocity - If we are the given the vertical and horizontal velocity of a moving projectile, we can find it's total velocity by using the Pythagorean Theorem (a^2 + b^2 = c^2). The velocities form a right triangle. The vertical and horizontal velocities are the legs and the total velocity is the hypotenuse. We can use the Pythagorean Theorem to find the hypotenuse, or in this case, the total velocity.
Example - If we square and add 7.6 m/s and 4.6 m/s we get 79.21 m/s, and square rooting that gives us a total velocity of 8.9 m/s.
d=1/2at^2 - This equation is used to find the distance an object travels when it's not moving at a constant velocity. This means that we use this equation to find vertical distance since vertical velocity is affected by acceleration due to gravity (g).
Example - Using this equation
Tangent - This is a trigonometric function used to find the angle measure of one of the angles in a triangle. This is found by dividing the opposite side by the adjacent side, then converting it into degrees by using an arctangent.
Example - To find tangent, we divide 7.6 m/s by 4.6 m/s. This is 1.65, and the arctangent of this number is about 59 degrees. This is the angle of the free throw.
Reflection
After 4 weeks of hard work, I feel somewhat satisfied with my contribution to this project. Some of my strengths were planning the script and keeping stability. During the project, after seeing the general video outline, I was able to create a script that flowed well with the video and not boring. I also chose different songs to be playing under the script, keeping the watchers interested, even during the calculations part. The script was generally balanced between the three of us, with Daniel talking about the free throw itself and Ash and I going back and forth about the physics. I was also able to keep everyone going in times of chaos. We sometimes got into arguments over what to put into the video, and I helped prevent it being detrimental the efficiency of the group.
But I definitely had some weaknesses. Some of my major problems were my contribution to the editing and the calculations. Ash did all the editing, and I didn't contribute as much as I thought I would to the editing. The editing is the most important part of creating the video, and I wished I could've stepped up and participated more in it. The calculations of the video were I thought were good at first, until my group found the error in the distances. I forgot to take into consideration that the ball must go in an arc to go into the hoop. This severe setback would force my group to rush and rerecord the video in the last day.
I feel that my contribution in this project wasn't very strong and that my Rube Goldberg contributions were much better. I hope to improve in the next project we do.
But I definitely had some weaknesses. Some of my major problems were my contribution to the editing and the calculations. Ash did all the editing, and I didn't contribute as much as I thought I would to the editing. The editing is the most important part of creating the video, and I wished I could've stepped up and participated more in it. The calculations of the video were I thought were good at first, until my group found the error in the distances. I forgot to take into consideration that the ball must go in an arc to go into the hoop. This severe setback would force my group to rush and rerecord the video in the last day.
I feel that my contribution in this project wasn't very strong and that my Rube Goldberg contributions were much better. I hope to improve in the next project we do.