Aquí puedes incluir un dato relevante a destacar
Graphical Representation
Introduction to Parabolas
Key Activity Juan Pablo A01738164 Santiago Rosas A01737954
Aquí puedes incluir un dato relevante a destacar
Application in Sports
Mathematical Analysis
References
Key Activity
Excel for Athletes
Parabolas
Excel makes it easy to analyze data. You enter your projectile's distance and height measurements into a spreadsheet. Then, Excel figures out the best-fit curve, which represents the parabolic path of the projectile. You can see this curve on a graph. Finally, Excel gives you the equation of the curve, so you can understand and predict the projectile's motion. It's a handy tool for understanding how parabolas work in real life.
A parabola is an open curve formed by intersecting a cone and a plane parallel to its side. It's defined as the path of a point equidistant from a fixed line (the directrix) and a fixed point (the focus). The vertex is the closest point to the directrix. Parabolas are symmetric about their axis and have various applications, such as describing projectile motion and architectural structures like bridges. The standard equation for a parabola with its vertex at the origin and axis along the x-axis is \(y^2 = 2px\), where \(p\) is the distance from the vertex to the focus.
Mathematical Procedure
Equation for 25%
Equation increased by 25%: y= -0.05757x^2+0.7052325
To adjust the trajectory of a thrown object, like a ball, to go farther while flying slightly lower, you tweak its original equation. It's like resizing and repositioning a picture to fit better. By stretching the equation horizontally to cover more ground and lowering its peak, you accurately model the changes in the object's flight. This updated equation reflects the new trajectory, showing how the ball flies farther but doesn't reach as high as before.
Excel for Athletes
Conclusion
In sports, math isn't just about analyzing performance; it's about optimizing training methods and refining strategies for better results. Parabolic trajectories, such as those observed in basketball shots and long jumps, exemplify how math is intricately woven into the fabric of athletic achievement. In addition, mathematical tools like Excel enable athletes and coaches to perform regression analysis, helping them understand and predict performance trends more accurately.
After engaging in activities related to parabolas and sports, one might find a deeper appreciation for their significance in real-world scenarios. This hands-on experience enhances understanding and perspective, offering valuable insights beyond classroom learning.
What are parabolas?
Real world application
Projectile Motion: The path of a thrown ball or a launched rocket follows a parabolic trajectory due to gravity.
Satellite Dishes: Satellite dishes are shaped like parabolas to efficiently focus incoming signals onto the receiver.
Solar Collectors: Parabolic mirrors concentrate sunlight onto a focal point in solar power systems for heating or electricity generation.
These examples highlight how parabolic shapes are utilized in different practical applications, from physics to technology and engineering.
A parabola is a curved shape formed when a plane intersects a cone. It's defined by points equidistant from a fixed line (the directrix) and a fixed point (the focus). The vertex is the closest point to the directrix, and the focus determines its shape. The axis is a line through the vertex and focus. It's symmetric, with a graceful curve receding from the axis.
Cartesian Plane
Key Activty Math
Juan Pablo Muñoz Ximénez
Created on April 26, 2024
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Transcript
Aquí puedes incluir un dato relevante a destacar
Graphical Representation
Introduction to Parabolas
Key Activity Juan Pablo A01738164 Santiago Rosas A01737954
Aquí puedes incluir un dato relevante a destacar
Application in Sports
Mathematical Analysis
References
Key Activity
Excel for Athletes
Parabolas
Excel makes it easy to analyze data. You enter your projectile's distance and height measurements into a spreadsheet. Then, Excel figures out the best-fit curve, which represents the parabolic path of the projectile. You can see this curve on a graph. Finally, Excel gives you the equation of the curve, so you can understand and predict the projectile's motion. It's a handy tool for understanding how parabolas work in real life.
A parabola is an open curve formed by intersecting a cone and a plane parallel to its side. It's defined as the path of a point equidistant from a fixed line (the directrix) and a fixed point (the focus). The vertex is the closest point to the directrix. Parabolas are symmetric about their axis and have various applications, such as describing projectile motion and architectural structures like bridges. The standard equation for a parabola with its vertex at the origin and axis along the x-axis is \(y^2 = 2px\), where \(p\) is the distance from the vertex to the focus.
Mathematical Procedure
Equation for 25%
Equation increased by 25%: y= -0.05757x^2+0.7052325
To adjust the trajectory of a thrown object, like a ball, to go farther while flying slightly lower, you tweak its original equation. It's like resizing and repositioning a picture to fit better. By stretching the equation horizontally to cover more ground and lowering its peak, you accurately model the changes in the object's flight. This updated equation reflects the new trajectory, showing how the ball flies farther but doesn't reach as high as before.
Excel for Athletes
Conclusion
In sports, math isn't just about analyzing performance; it's about optimizing training methods and refining strategies for better results. Parabolic trajectories, such as those observed in basketball shots and long jumps, exemplify how math is intricately woven into the fabric of athletic achievement. In addition, mathematical tools like Excel enable athletes and coaches to perform regression analysis, helping them understand and predict performance trends more accurately.
After engaging in activities related to parabolas and sports, one might find a deeper appreciation for their significance in real-world scenarios. This hands-on experience enhances understanding and perspective, offering valuable insights beyond classroom learning.
What are parabolas?
Real world application
Projectile Motion: The path of a thrown ball or a launched rocket follows a parabolic trajectory due to gravity. Satellite Dishes: Satellite dishes are shaped like parabolas to efficiently focus incoming signals onto the receiver. Solar Collectors: Parabolic mirrors concentrate sunlight onto a focal point in solar power systems for heating or electricity generation. These examples highlight how parabolic shapes are utilized in different practical applications, from physics to technology and engineering.
A parabola is a curved shape formed when a plane intersects a cone. It's defined by points equidistant from a fixed line (the directrix) and a fixed point (the focus). The vertex is the closest point to the directrix, and the focus determines its shape. The axis is a line through the vertex and focus. It's symmetric, with a graceful curve receding from the axis.
Cartesian Plane