Chapter 9.6, Problem 2P

To determine

Find the distance of landing of ball from the batter.

Answer to Problem 2P

About 144.8 feet.

Explanation of Solution

Given :

A batter strikes a baseball . The equation $y=-0.005x^2+0.7x+3.5$ 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 :

  $y=-0.005x^2+0.7x+3.5$

When the ball lands, its height will be 0.

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

  $\begin{array}{l}-0.005x^2+0.7x+3.5=0\\ \Rightarrow -5x^2+700x+3500=\mathrm{0...............}[\text{multiply each side by 1000]}\\ \Rightarrow x^2-140x-700=\mathrm{0.....................}[\text{divide each side by -5]}\end{array}$

Comparing the equation with standard quadratic equation , a = 1, b = -140 , c = -700

Find roots using the quadratic formula:

  $\begin{array}{l}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ \Rightarrow x=\frac{-(-140)\pm \sqrt{{(-140)}^2-4(1)(-700)}}{2(1)}\\ \Rightarrow x\approx 144.8\text{ ft}\text{.}\end{array}$

Since the distance is positive, so the distance of landing of ball is about 144.8 feet.