Analysis of a Moving Object

By: Sydney Sauer

Introduction to the Study

The basketball was first invented in the year of 1891 in Springfield Massachusetts by a physical education teacher from Canada named James Naismith. He invented it in hopes to create a new sport that was less injury-prone than football. Throughout the 20th century the game popularized in America and other countries very quickly. Collegiate teams were soon formed followed by the establishment in 1942, of a professional NBA league. The NBA had grown into a multi-million dollar enterprise by the end of the 20th century along with becoming an impact part of American entertainment, sport and culture.

The purpose of this study is to analyze the the constant and accelerated velocity of a basketball based off videos that I have created. The importance in finding the constant velocity is to understand the highest meter per second that the ball is traveling in the video. The importance in finding the velocity of the ball accelerating (the movement of the ball starting when I push the ball and when it starts to accelerate) is to understand how quickly the ball moves a specific distance over an amount of time after being pushed.

To video tape these two different actions I set a meter stick out in the hallway on the floor to represent the distance that the ball would be traveling when I later had to graph the information in logger pro. Another student video-taped me in one video rolling the ball from left to right at both a constant speed and from a rest to constant speed. I rolled the ball from left to right in both videos because when graphing in logger pro, I was able to plot an origin in a specific place that allowed me to have a positive velocity. As I graphed my data from the video I plotted my points in the middle most front part of the basketball to receive the most accurate and best plotted data possible.

Constant Ball Movement - Position vs. Time

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Constant Ball Movement - Velocity vs. Time

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Analysis of Constant Ball Movement

In both of my graphs for the constant ball movement I used x position and x velocity because when analyzing the video the ball moved from left to right across the origin which is the x direction. I will gather the information I need to find velocity of the constant ball movement from the position vs. time graph. The reason I am using this graph to gather my information is because it offers an accurate set of consistent points that would be most reasonable to create a slope equation from. The equation I am going to use to show the slope and y- int, is y=mx+b. This equation can help us understand the linear relationship between each point and best explain why each point is in a certain spot on the graph. The equation from the x position vs. time graph is Position(x)=1.803 m/s*time(s) + (-2.756 m).

Quantitative

The equation I collected Position(x)=1.803 m/s*time(s) + (-2.756 m) explains the relationship of how the independent variable of time, effects the dependent variable of distance in meters. The position in this situation increases 1.803 meters per second. The y intercept is -2.756 m. This means that the starting position was 2.756 meters behind the origin.

Qualitative

Once the ball gets to the meter stick it has reached its maximum acceleration that it could possibly have based on the power of my hand rolling it. This velocity of 1.803 m/s is the velocity that it holds throughout the entire constant trial. I can back this up because while recording, the ball did not look as if it sped up or slowed down at all. (It eventually slowed down but I did not record that part because it was irrelevant to what we were trying to find and graph).

Extension

I was interested in finding out what the position of my ball would be at 20 seconds. To find that I replaced 20 in for the x value of time (s) in my equation when the velocity remained at 1.803 meters per second and when the starting position is 2.756 meters behind the origin. After replacing and calculating I came up with the number of 33.304 meters as the position that my ball would be in at the time of 30 seconds.

Accelerated Ball Movement - Position vs. Time

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Accelerated Ball Movement - Velocity vs. Time

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Analysis of Accelerated Ball Movement

In both of my graphs for the accelerated ball movement I also used the x position and x velocity graphs because when analyzing the video the ball moved from left to right across the origin which is the x direction. Although it would be most common for someone to use the x position vs. time graph to find an equation and describe the linear relationship for the points, I will be using the x velocity vs. time graph. My reasoning for this is because even though my position graph has a y-int that would be closer to zero (where it should be as a starting position) the increase in slope is not very high per second making it difficult to notice the change in speed over time. This could lead someone to think that the ball was not moving at all because the number is so low. Therefore I will be using the x velocity vs. time graph. Only the highlighted points will be analyzed for the equation because they best show the ball at its rest then the increase from that point to where it reaches a constant speed. I will be using the same equation that I used to show the constant ball movement; y=mx+b. This equation can help us gather information that is needed to explain the linear relationship between each of the plotted points. The position for the x velocity vs. time graph is X (velocity m/s)=1.698 m/s/s*time (s)+(-0.9715).

Quantitative

The equation I collected X(velocity m/s)=1.698 m/s/s*time(s)+(-0.9715 m/s) can explain the relationship of how the independent variable of time, effects the dependent variable of velocity in m/s. As time increases the velocity changes. Based off the graph, the acceleration was 1.698 m/s/s. This means for every second that the ball travels the acceleration will increase 1.698 meters per second. The y-int for my equation is -0.9715. My goal was to have a y-int start at 0 m/s to begin, but unfortunately that is not what happened when I retrieved my data from the graph. Because my y-int is -0.9715 it means that I must have rolled the ball backwards in the video before I rolled it forwards and plotted points to follow that movement.

Qualitative

As I am accelerating in this video my velocity is increasing. In the beginning of the video my ball is at rest. My numbers did not show that it was at rest but it is what it should have been at. As the ball leaves its rest position it moves towards its highest possible acceleration (creating a velocity) that it can possibly reach. This final velocity will not match the velocity in my constant graph because I used two different videos of me rolling the ball which means the ball will have a different acceleration in each video.

Extension

What I really wanted to know was at the time of 48 seconds what the velocity would be of my ball if the acceleration remained at 1.698 m/s/s and my y-int (or starting point) remained as -0.9715. When I plugged in the number to the equation my answer was 80.5325 m/s. This is the velocity of the ball at 48 seconds.

Displacment

First, what is displacement? Well displacement is the moving of something from its original place or position and where it is at a given time. In both videos the ball is moving left to right which means the displacement should be positive because I never moves backwards towards the right, therefore the distance (the amount traveled measured in units) traveled would be the displacement.

Closing

In conclusion I achieved what I had set out to do. The purpose of my study was to analyze the the constant velocity and accelerated acceleration of a basketball based off videos that I have created. I was able to successfully do this by properly analyzing the graphs, getting an equation from each graph showing how the velocity or acceleration is created and why it is what it is. To over cap the situation the equation from the constant graph states the velocity as the slope which is 1.803 m/s. The acceleration for the accelerated graph is 1.698 m/s/s.

Some of the experimental errors that I could have encountered were possibly mis-placing points or plotting points starting on the left hand side of the origin. Unfortunately I did do this one the both the accelerated and constant data, causing me to have a negative y-int. Some of the human errors that could have occurred are not using the right graph to gather an equation from or even taking a poor video. Based of the points on all my graphs I believe I used the correct graphs to pull my information from (although I could have collected better videos which would give me better accuracy on my equations).

I can apply this to the real world as I did in my extension to predict what the position would be with the constant equation and what my velocity of the ball would be at a certain point with the accelerated equation. This can help us in the real world of science to predict where things have the possibility to move to over a certain point of time. It can be applied to things such as cars, boats (the engineering of these things) or even sports.