Chapter 3.1, Problem 28E

a)

To determine

To explain: $h$ is a function of $t$ .

Answer to Problem 28E

  $h$ is a function of $t$ because the $h$ is a dependent variable on the $t$ .

Explanation of Solution

Given information:

  

We can see in the figure clearly that $h$ is a dependent variable on the $t$ .

Hence, $h$ is a function of $t$ .

b)

To determine

To find: Get the height of the projectile.

Answer to Problem 28E

The height of projectile after $0.5\sec \&1.25\sec$ is $20\&28$ respectively.

Explanation of Solution

Given information:

  

Calculation: Draw the parabolas at $x=0.5\&x=1.25$ .

Hence the approximate values of $h\left(0.5\right)\&h\left(1.25\right)$ :

  $\begin{array}{l}h\left(0.5\right)\approx 20\\ h\left(1.25\right)\approx 28\end{array}$

c)

To determine

To find: The domain

Answer to Problem 28E

The domain of the function is $x\in \left[0,2.7\right]$ .

Explanation of Solution

Given information:

  

Calculation: Get the domain of the function,

  $\begin{array}{l}0\le x\le 2.7\\ x\in \left[0,2.7\right]\end{array}$

Therefore, the domain of the function is $x\in \left[0,2.7\right]$ .

d)

To determine

To explain: $t$ is a function of $h$ .

Answer to Problem 28E

  $t$ is not a function of $h$ .

Explanation of Solution

Given information:

  

Since $h$ has two different corresponding values for $t$ , hence, $t$ is not a function of $h$ .