Research To complete this worksheet you will need to find similar statistics (sp

Question

Research

To complete this worksheet you will need to find similar statistics (speed and estimated height) for another tall fountain in the world so you can determine how long you expect its water to stay in the air and whether or not the height that is indicated matches your parabola. While conducting your research, also make note of the name of the fountain (if any) and where it is located (city, country). Possible search phrase: World Highest Fountains.

Data Collection

1. What is the name (if any is specified) of the fountain you have chosen?

2. Where in the world is it located (city, country)?

3. What is the velocity (speed) at which it projects water?

If speed is given in miles per hour, follow the 2 step conversion process, showing your work below, to arrive at the number of feet per second.

Step 1: Multiply the miles per hour given by the number of feet in a mile.

Step 2: Divide the above feet per hour by the number of seconds in an hour.

Indicate the feet per second (velocity) of your fountain.

Feet per second (v)

4. What is the height the water from the fountain reaches into the air?

5. Most power fountains begin at ground level (starting height (s) = 0). If that is not the case with your chosen fountain, what is the starting height indicated?

If the starting height is not specified in the research, provide your best estimate for starting height.

Starting Height (s)

Writing the Quadratic Equation

6. Substitute the data from 3 (v) and 5 (s) above into their proper position in the formula y = –16x2 + vx + s and write the formula in the space provided below.

The equation for this fountain is:

How Long Will the Water Remain in the Air?

7. Use the graphing technology of your choice to graph the above equation and determine the x-intercept values. Set rounding to 5 places. Save a copy of this graph and paste or attach it to this Worksheet.

8. What are the x-intercept values?

9. How long does this mean the water from your fountain will remain in the air?

How High Will the Water Reach?

10. Identify the a, b, and c values in your equation.

a =

b =

c =

11. What is the formula for locating the x-coordinate of the vertex?

12. Use the graphing technology of your choice to graph the above equation and find the vertex value. Set rounding to 5 places. Save a copy of this graph and paste or attach it to this Worksheet.

13. What are the coordinates of the vertex?

14. How high does this mean the water from your fountain reaches into the air?

15. Does this match the height indicated by your research?

Yes
No

16. If it is different, what do you think may be a possible reason why the two numbers differ?

Explanation / Answer

One type of air blower can fill a blimp (or dirigible) in six hours working alone, while a second blower fills the same blimp in nine hours working alone. Working together, how long will it take both blowers to fill the blimp?

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