Chapter 3.1, Problem 28E

i.

To determine

To Explain: The graph represents the height $h$ of a projectile after $t$ seconds.

  

Explain why $h$ is a function of $t$ .

Explanation of Solution

Here we can see that as time changes, height also changes with respect to time, so we can say that the value of $h$ depend on the value of $t$ . Hence $h$ is function of $t$ .

ii.

To determine

To calculate: The graph represents the height $h$ of a projectile after $t$ seconds.

  

Approximate the height of the projectile after 0.5 seconds and after 1.25 seconds.

Answer to Problem 28E

  $h\left(0.5\right)\approx 20$

  $h\left(1.25\right)\approx 27$

Explanation of Solution

Calculation: First we find the value of $h$ when $t=0.5$

in above graph draw a line parallel to $y-axis$ which passes through $t=0.5$

from above graph we can see that $h\approx 20$ when $t=0.5$

so, $h\left(0.5\right)\approx 20$

Now, we find the value of $h$ when $t=1.25$

in above graph draw a line parallel to $y-axis$ which passes through $t=1.25$

from above graph we can see that $h\approx 27$ when $t=1.25$

so, $h\left(1.25\right)\approx 27$

iii.

To determine

To calculate: The graph represents the height $h$ of a projectile after $t$ seconds.

  

Approximate the domain of the function.

Answer to Problem 28E

Domain of the given function is $t\in \left[0,2.7\right]$

Explanation of Solution

Calculation: Now we find the domain of the function, domain of a function is collection of all values of $t$ for which we can find the values of $h$ .

here, $t$ varies from 0 to 2.7,

so, the domain of the function is $0\le t\le 2.7$ , i.e. $t\in \left[0,2.7\right]$

iv.

To determine

To calculate: The graph represents the height $h$ of a projectile after $t$ seconds.

  

Is $t$ a function of $h$ ? Explain.

Explanation of Solution

No, $t$ is not function of $h$ or we can say that $t$ is not even function because for one value of $h$ we have 2 values of $t$ . So $t$ cannot be a function.