Pre-Calc: Ch. 3 Extension Problem

For my high school pre-calc class.

Transcript

1. Chapter 3 Extension Tossing a Ball Chris Henn 10/9/11
2. The problem Toss a ball from a set location. Keep track of where it lands and how high it goes.
3. Data 1 2 3 4 5 6 7 8 9 10 11 height at peak length of toss 2.1 2.0 2.1 2.2 2.1 2.0 1.9 2.2 1.9 2.0 2.1 1.4 1.4 1.5 1.4 1.5 1.6 1.8 1.3 1.4 1.5 1.6 Trial Result
4. Find averages Average length of throw: Average peak height: 2.05m 1.49m
5. Find the equation y = ax 2 + b 0 = a( 2.05 2 )2 + 1.49 a = 1.42 y = 1 . 42 x 2 + 1 . 49 Quadratic equation, represents path of ball
6. Graph equation -2.4 -2 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6 2 2.4 -0.8 -0.4 0.4 0.8 1.2 1.6 2 Average height at peak (0,1.49) Average distance from peak landing point (1.025,0)
7. Area under the ball Represented by the equation: a ( x ) = 2 a 3 x 3 + bx 2 + 2 cx With our values plugged in: a ( x ) = ( 2 · 1 . 42 3 )1 . 0253 + 2(1 . 49)(1 . 025)
8. Therefore... Area under the ball is 2.06m2
9. Blank Slide!