Algebra 50 - Three Variable Systems in the Real World - Problem 2

TL;DR

Using a system of three linear equations, A.V. Geekman determines the equation for his parabolic trajectory and achieves a new altitude record.

Transcript

Hello. I'm Professor Von Schmohawk and welcome to Why U. In the last lecture, we saw how a system of three linear equations in three variables could be used to solve a problem with three unknown quantities the price of a ticket the price of a drink and the price of popcorn. We knew that three different groups of people had purchased different quant... Read More

Key Insights

• 🚱 Systems of three linear equations in three variables can be used to solve problems involving non-linear equations, such as parabolic trajectories.
• 😥 Substituting the coordinates of multiple points into the equation for a parabola creates a system of linear equations.
• 😃 The variables in the system of linear equations represent the coefficients A, B, and C that determine the shape of the parabolic trajectory.
• 🥺 The system of linear equations can be solved by eliminating variables one by one, leading to the unique values of A, B, and C.
• 😥 Graphing the equation for the parabolic trajectory allows for visualization and determination of maximum or minimum points.
• 😥 By recording multiple points and creating a system of equations, it is possible to calculate the unique solution for unknown quantities in non-linear equations.
• 😘 Converting the equation for a parabola to vertex form simplifies determining the highest or lowest points on the parabola.

Questions & Answers

Q: How does the camera help A.V. Geekman determine the equation for his parabolic trajectory?

The camera captures three images of A.V.'s flight at different points, providing him with the x and y coordinates of these positions. By substituting these values into the equation for a parabola, A.V. can create a system of three linear equations.

Q: Why are the variables A, B, and C not squared in the system of linear equations?

In the equation for a parabola, A, B, and C are the coefficients that determine the dimensions and orientation of the parabola. These are the unknown quantities that need to be calculated, not the squared variables x and y.

Q: How is the system of linear equations solved to determine the values of A, B, and C?

The system is solved by eliminating variables one by one. By combining equations and performing operations, the values for A, B, and C can be determined. In this case, eliminating C is done first, followed by eliminating A and solving for B, and finally substituting the values back into the original equations to find C.

Q: How does A.V. Geekman use the equation for his parabolic trajectory to determine his maximum altitude?

By graphing the equation, A.V. can visualize the path of his parabolic trajectory. He can observe that it passes through all three recorded points and determine the maximum point, which corresponds to the highest altitude reached during his flight.

Summary & Key Takeaways

• Professor Von Schmohawk explains how a system of three linear equations in three variables can be used to solve a real-world problem involving a parabolic trajectory.

• A.V. Geekman aims to break the altitude record at Why U by launching himself with a slingshot, and uses a camera to capture three points of his flight.

• By substituting these points into the equation for a parabola, A.V. creates a system of three linear equations that can be solved to determine the values of A, B, and C.