Chapter 9.6, Problem 22PPE

To determine

Find the distance of landing of ball from the batter.

Answer to Problem 22PPE

About 252.5 feet.

Explanation of Solution

Given :

A football player punts a ball . The equation $y=-0.004x^2+x+2.5$ models its path , where x is the horizontal distance, in feet, the ball travels and y is the height, in feet , of the ball .

Calculation:

Given :

  $y=-0.004x^2+x+2.5$

When the ball lands, its height will be 0.

Substitute y = 0 in the equation and solve for x :

  $-0.004x^2+x+2.5=0$

Comparing the equation with standard quadratic equation , a = -0.004, b = 1 , c = 2.5

Find roots using the quadratic formula:

  $\begin{array}{l}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ \Rightarrow x=\frac{-1\pm \sqrt{1^2-4(-0.004)(2.5)}}{2(-0.004)}\\ \Rightarrow x=\frac{-1\pm \sqrt{1+0.04}}{-0.008}\\ \Rightarrow x=\frac{-1\pm \sqrt{1.04}}{-0.008}\\ \Rightarrow x=\frac{-1\pm 1.02}{-0.008}\\ \Rightarrow x\approx 252.5\text{ ft}\text{.}\end{array}$

Since the distance is positive, so the distance of landing of ball is about 252.5 feet.