Chapter 8, Problem 15CT

a.

To determine

To find: The maximum height of the tennis ball.

Answer to Problem 15CT

Maximum height is 4.445 feet.

Explanation of Solution

Given information: The quadratic function $y=-0.005x^2+0.17x+3$

Formula used:

The x coordinate of vertex is given by formula $\frac{-b}{2a}$ . The y coordinate of vertex is $f(\frac{-b}{2a})$ .

Calculation:

Here, find the y coordinate of vertex.

From the given equation,

  $\begin{array}{l}a=-0.005\\ b=0.17\end{array}$

Plug in these values into the formula to find x coordinate of vertex.

  $\frac{-b}{2a}=\frac{-0.17}{2(-0.005)}=17$

Now, plug in x as 17 into the equation to find corresponding y .

  $y=-0.005{(17)}^2+0.17(17)+3$

  $=-1.445+2.89+3$

  $=4.445$

b.

To determine

To Explain: The ball clears the net or not.

Answer to Problem 15CT

The ball can clear the net because ball will go 3.6 feet but the height of the net is 3feet.

Explanation of Solution

Given information: You are standing 30feet from the net and height of the net is 3ft.

Calculation:

We have $y=-0.005x^2+0.17x+3$ , putting x = 30 will give

  $\begin{array}{l}y=-0.005x^2+0.17x+3\\ \Rightarrow y=-0.005{\left(30\right)}^2+0.17\left(30\right)+3\\ \Rightarrow y=-4.5+5.1+3\\ \Rightarrow y=3.6\end{array}$

As 3.6 > 3 , thus the ball will clear the net