Chapter 9.2, Problem 37PPS

a.

To determine

How long is she in the air.

Answer to Problem 37PPS

  $2.2\text{ seconds}$

Explanation of Solution

Given:

The equation that models her height h , in feet, in the air after t seconds is given by $h=-16t^2+30t+10$ .

Calculation:

In order to find the time she was in the air, set the height equal to 0 and solve for t values. Because when she will come back to ground, her height will be 0 feet.

So, now plot the graph of the given height function and find the x -intercept.

The graph of the function is shown below:

  

From the above graph it is clear that the x -intercept is approximately at 2.2, so she was in the air for 2.2 seconds.

b.

To determine

When will she reach a height of 15 feet.

Answer to Problem 37PPS

  $\text{After }0.2\text{ seconds and 1}\text{.7 seconds}$

Explanation of Solution

Given:

The equation that models her height h , in feet, in the air after t seconds is given by $h=-16t^2+30t+10$ .

Calculation:

In order to find the time when she was at a height of 15 feet, plot the graph and check the points when the height of the graph is 15 feet.

The graph of the function is shown below:

  

From the above graph it is clear that she was at a height of 15 feet twice. Once going up after 0.2 seconds and once coming down after 1.7 seconds.

c.

To determine

Whether she earned bonus point or no which can be earned on reaching a height of 20 feet.

Answer to Problem 37PPS

  $Yes$

Explanation of Solution

Given:

The equation that models her height h , in feet, in the air after t seconds is given by $h=-16t^2+30t+10$ .

Calculation:

In order to check whether she got the bonus point or no, plot the graph of the function and check whether she went beyond the height of 20 feet or no.

The graph of the function is shown below:

  

From the above graph it is clear that maximum height attained by her is approximately 24 feet, which is more than 20 feet.

So, yes she earned the bonus points.