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College Algebra Math 130

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Every year, Millsboro, Delaware, hosts the World Championship Punkin’ Chunkin’, where participants launch pumpkins using catapults. This competition allows us to explore physics through the motion of a pumpkin, modeled by the equation y = -16t² + vt + h. We can create a quadratic function to determine the pumpkin's height over time, analyze when it hits the ground, and find its maximum height and other key moments. This hands-on example connects math to real-world applications, making learning algebra engaging and fun.

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College Algebra Math 130

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  1. College AlgebraMath 130 Amy Jones Lewis

  2. Punkin’ Chunkin’ • Every year, the city of Millsboro, Delaware, holds a competition called the World Championship Punkin’ Chunkin’, which is a pumpkin throwing competition. Participants build a pumpkin catapult that hurls a pumpkin. The catapult that hurls the pumpkin the farthest is the winner.

  3. Punkin’ Chunkin’ http://www.youtube.com/watch?v=559yuhpsd4Y&feature=related

  4. Punkin’ Chunkin’ • You can model the motion of a pumpkin that is released by a catapult by using the vertical motion model y = -16t2 + vt +h,where • tis the time that the object has been moving in seconds • vis the initial velocity of the object in ft per sec. • his the initial height of the object in feet • yis the height of the object in feet at time t seconds.

  5. Punkin’ Chunkin’ • Suppose that a catapult is designed to hurl a pumpkin from a height of 30 feet at an initial velocity of 212 feet per second. • Write a quadratic function that models the height of the pumpkin in terms of time.

  6. Punkin’ Chunkin’ • Write an equation that you can use to determine when the pumpkin will hit the ground. • Solve the equation. • Do both solutions have meaning in the problem situation?

  7. Punkin’ Chunkin’ • What is the height of the pumpkin three seconds after it is launched from the catapult? • What is the height of the pumpkin eight seconds after it is launched from the catapult? • What is the height of the pumpkin 20 seconds after it is launched from the catapult?

  8. Punkin’ Chunkin’ • When is the pumpkin at its highest point? • What is the maximum height of the pumpkin? • When is the pumpkin at a height of 500 feet? • Is your answer confirmed by your graph?

  9. Monday’s Grocery Shopping • On Monday, you shoot a .280 Remington with a 165 grain bullet, which has an initial velocity of 2820 feet per second. • Given that you miss trees, deer, and other hunters, when will your bullet hit the ground?

  10. Homework Next Class: Wednesday, December 1 Happy Thanksgiving!

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