Chapter 3.1, Problem 60E

a.

To determine

To find and interpret the zeros of the function and then sketch the graph using zeros.

Answer to Problem 60E

The zeros are $t=\pm \frac{7}{2}$ .

Explanation of Solution

Given:

  $h\left(t\right)=196-16t^2$

Calculation:

To find the zeros, put $h\left(t\right)=0$ .

  $\begin{array}{c}196-16t^2=0\\ 16t^2=196\\ t^2=\frac{196}{16}\\ t=\pm \frac{14}{4}\end{array}$

Thus, $t=\pm \frac{7}{2}$ .

The zeros of the function is the time when the weight hits the ground (when height $h$ is zero).

Since, time cannot be negative, $t=\frac{7}{2}$ .

Now sketch the graph using the zeros of the function $h\left(t\right)=196-16t^2$ .

For $t=0$ , $h\left(t\right)=196$ .

Thus, the vertex of the graph lies at $\left(0,196\right)$ .

b.

To determine

To explain what does domain and range of the function represents.

Answer to Problem 60E

The domain is the time (in seconds) when the weight is falling. The range is the height as the weight falls to the ground.

Explanation of Solution

The domain is the time (in seconds) when the weight is falling. The range is the height as the weight falls to the ground.