IB Math IA: Basketball Shot Quadratic | IB Math IA | Mr. Flynn IB

Mr. Flynn IB
25 Sept 202008:04

TLDRIn this educational video, Mr. Flynn demonstrates how to create a quadratic function using a basketball shot video. He utilizes Logger Pro Demo to analyze the trajectory, scales the video with a known object for accuracy, and plots the basketball's path. The video concludes with a quadratic equation representing the shot's parabolic trajectory. Mr. Flynn plans to use calculus and quadratic knowledge to further analyze the shot in future lessons, exploring concepts like launch angle and maximum height.

Takeaways

  • 🏀 The video demonstrates creating a quadratic function from a basketball shot video using Logger Pro software.
  • 📝 The instructor opens Logger Pro demo and imports a basketball shot video taken from the side to ensure a straight line perspective.
  • 🎥 The video is paused at the moment the basketball is released to define the starting point of the projectile motion.
  • 📏 A foam roller of known length (90 cm) is used to scale the video for accurate measurements.
  • 📐 Axes are set with the origin at the feet of the person shooting and aligned with the bottom of the net for the y-axis, representing the basketball's path.
  • 📈 The instructor captures points along the basketball's trajectory to plot a graph showing the parabolic shape of the shot.
  • 📊 The x-axis represents horizontal distance, while the y-axis represents vertical distance, both in meters.
  • 🔍 Logger Pro's curve fit feature is used to fit a quadratic function to the plotted points.
  • 📘 The resulting quadratic function is given by y = -0.3133x^2 + 1.198x + 2.137, representing the basketball's trajectory.
  • 📚 The significance of the coefficients (a, b, c) in the quadratic function is discussed in terms of the basketball's path.
  • 📈 The instructor plans to analyze the function further in the next lesson, using calculus and quadratic knowledge to explore concepts like maximum height and launch angle.
  • 🤓 The video aims to show how the quadratic function can be used in an IB Math IA to compare shots or suggest improvements.

Q & A

  • What is the main purpose of the video?

    -The main purpose of the video is to create a quadratic function from a basketball shot video using Logger Pro software.

  • What software is used in the video to analyze the basketball shot?

    -Logger Pro is the software used in the video to analyze the basketball shot and create a quadratic function.

  • How does the video ensure the basketball shot is captured from a straight line perspective?

    -The video ensures the basketball shot is captured from a straight line perspective by filming from the side, aligning the shooter's feet with the basket.

  • What is the significance of using a foam roller in the video?

    -The foam roller, which is known to be exactly 90 centimeters, is used as a reference to scale the video in Logger Pro for accurate measurements.

  • Why is the video clip not starting at zero seconds?

    -The video clip does not start at zero seconds because it was not edited to do so. The instructor suggests clipping the video to start at zero for better analysis.

  • What is the shape of the graph representing the basketball shot's trajectory?

    -The shape of the graph representing the basketball shot's trajectory is parabolic, which is typical for projectile motion.

  • How does the instructor select points for the quadratic function on the Logger Pro?

    -The instructor selects points for the quadratic function by clicking on the basketball's position in the video frame by frame and marking the center of the basketball on the y-axis.

  • What does the instructor do to fit a quadratic curve to the data points?

    -The instructor uses the 'curve fit' feature in Logger Pro and selects a quadratic function to fit the data points.

  • What are the coefficients of the quadratic function obtained from the video analysis?

    -The coefficients of the quadratic function are a = -0.315, b = 1.198, and c = 2.137.

  • What will be covered in the next lesson according to the video?

    -In the next lesson, the instructor plans to analyze the quadratic function using calculus and knowledge of quadratics to find maximums, launch angles, and discuss how the shot could be improved or compared to others.

  • Why is the instructor not concerned with the red quadratic in the Logger Pro graph?

    -The instructor is not concerned with the red quadratic because it is not relevant to the analysis. The focus is on the y-values representing the vertical position of the basketball.

Outlines

00:00

🏀 Creating a Quadratic Function from a Basketball Shot Video

In this segment, the creator introduces a project to develop a quadratic function based on a basketball shot video. They begin by opening Logger Pro Demo, a software for data analysis, and proceed to import a video of a basketball shot taken from the side. The video is aligned to ensure a direct view of the shot trajectory. The creator emphasizes the importance of scaling the video with a known reference object, a 90 cm foam roller, to ensure accurate measurements. They then set up a coordinate system with the origin at the feet of the player and the basketball on the y-axis. The process involves capturing the basketball's trajectory frame by frame to plot points on the coordinate system, ultimately forming a parabolic shape indicative of a projectile motion.

05:01

📈 Analyzing the Basketball Trajectory with a Quadratic Curve Fit

This paragraph focuses on analyzing the basketball's trajectory using the data collected from the video. The creator converts the time-based x-axis to meters to align with the vertical y-axis, both measured in meters, for a more straightforward analysis. They utilize Logger Pro's curve fitting tool to fit a quadratic equation to the plotted points, resulting in the equation y = -0.3133x^2 + 1.198x + 2.137. The creator simplifies the coefficients for clarity and discusses the importance of mathematical notation. The summary concludes with a preview of future lessons, where the creator plans to explore the implications of the derived quadratic function using calculus and further analysis to understand aspects like launch angle and shot optimization.

Mindmap

Keywords

💡Quadratic function

A quadratic function is a polynomial function of the form y = ax^2 + bx + c. In the video, the presenter uses a quadratic function to model the trajectory of a basketball shot. This function helps in analyzing the parabolic path the basketball follows.

💡Logger Pro

Logger Pro is a data-collection and analysis software used to analyze video and other experimental data. The presenter uses Logger Pro to import and analyze the video of the basketball shot, demonstrating how to fit a quadratic curve to the trajectory of the ball.

💡Projectile

A projectile is an object thrown into space upon which the only force acting is gravity. In the video, the basketball is treated as a projectile, and its motion is analyzed to create a quadratic function that represents its path.

💡Scale

In the context of the video, scaling refers to setting a known distance in the video to ensure accurate measurements. The presenter uses a foam roller of known length to scale the video, allowing for precise distance measurements of the basketball's trajectory.

💡Axes

Axes refer to the coordinate system used for plotting data points. The presenter sets up the x and y axes in Logger Pro, with the origin at the shooter's feet, to accurately plot the basketball's path and create the quadratic function.

💡Curve fit

Curve fitting is the process of adjusting a curve to fit a set of data points. In Logger Pro, the presenter uses the curve fit function to apply a quadratic equation to the plotted points of the basketball's trajectory, resulting in the quadratic function that models the shot.

💡Parabolic shape

A parabolic shape is the curved shape of a parabola, which is the graph of a quadratic function. The basketball's trajectory follows a parabolic shape, which is why a quadratic function is suitable for modeling its path.

💡Significant figures

Significant figures are the digits in a number that carry meaning contributing to its precision. The presenter discusses the significance of using appropriate significant figures when noting the coefficients of the quadratic function, ensuring the function is accurately represented.

💡Launch angle

The launch angle is the initial angle at which a projectile is released. The presenter mentions that in the next lesson, they will analyze the quadratic function to determine the launch angle of the basketball, which is crucial for understanding the shot's trajectory.

💡Maximum

The maximum refers to the highest point on the parabolic path of a projectile. The presenter indicates that further analysis of the quadratic function will involve finding the maximum height reached by the basketball, which is an important aspect of projectile motion.

Highlights

Introduction to creating a quadratic function from a basketball shot video.

Using Logger Pro Demo for data analysis.

Importing a basketball shot video into Logger Pro.

Aligning the video to ensure a side view for accurate trajectory analysis.

Identifying the starting point of the projectile motion.

Scaling the video using a known length object, a foam roller.

Setting up axes with the origin at the feet and aligned with the net.

Capturing the basketball's trajectory by frame-by-frame analysis.

Creating a set of points to represent the basketball's path.

Choosing the Y-axis to represent the vertical distance.

Fitting a quadratic curve to the basketball's trajectory data.

Conversion of time to meters for the X-axis to simplify the model.

Determining the coefficients of the quadratic function: a, b, and c.

Formulation of the quadratic function representing the basketball shot.

Discussion on significant figures and decimal places in the context of the model.

Application of the quadratic function in further analysis using calculus.

Practical applications of the model in improving basketball shooting techniques.

Teaser for the next lesson on analyzing the quadratic function for insights.

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