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Understanding Rebound Ratios: A Study of Bounciness in Sports Balls

In this chapter, we explore the mathematics behind rebound ratios, specifically focusing on the bounciness of different sports balls. Through the analysis of functions like f(x) = 1.5x² - 0.9x + 11.5 and g(x) = -0.2x² - 0.4x + 2.8, we will determine the missing terms and rules for each function. We will also calculate rebounding ratios for basketballs, tennis balls, soccer balls, and squash balls under specific conditions. Understanding bounce dynamics is crucial for game performance and ball design standards.

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Understanding Rebound Ratios: A Study of Bounciness in Sports Balls

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  1. Chapter 2.1.2 Rebound Ratios

  2. Algebra Review: • Find the POI. f(x) = 1.5x2- 9x + 11.5 g(x) = -0.2x2- 0.4x + 2.8

  3. Find the missing terms and write a rule for each exponential function.

  4. How High Will It Bounce? • Many games depend on how a ball bounces. For example, if different basketballs rebound differently, one basketball would bounce differently off of a backboard than another would, and this could cause basketball players to miss their shots. For this reason, manufacturers have to make balls’ bounciness conform to specific standard. • Listed on the next slides are the “bounciness” standards for different kinds of balls.

  5. 2-20 continued • Tennis Balls: Must Rebound approximately 111 cm when dropped from 200 cm. What is the rebounding ratio? • Soccer balls: Must rebound approximately 120 cm when dropped from 200cm onto a steel plate. What is the rebounding ratio?

  6. NOW DETERMINE THE REBOUNDING RATIO FOR THE FOLLOWING BALLS. Basketballs: Must rebound approximately 53.5 inches when dropped from 72 inches onto a wooden floor. Squash Balls: Must rebound approximately 29.5 inches when dropped from 100 inches onto a steel plate at 70 degrees Fahrenheit.

  7. A new bouncing ball • Plot these values. • Should the points be connected? • Describe the independent variable • Describe the dependent variable. • State the equation to fit the data. • Should point (0,0) be included?

  8. On your own • Read and take notes on • Methods and Meanings • Page 62 Do Review and Preview Pg 62 #26-29 and 37-41

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