Diving into Math
at
Lake Powell
Open Upon Arrival
Math at Powell
Name
You made it to Powell. It is probably hot and you are waiting around for your parents
to take care of everything, so put on your swimsuit and go jump off the marina (make
sure the water is deep enough or just pretend to jump).
The path of your dive can be modeled by the equation y = -16t2 + 8t
Fill in the table:
Now explain the meaning of the “t” and “y” values.
Not sure? Perhaps a graph would help. Create a graph using the points.
When do you hit the water?
How do you know that?
What is the highest you jump?
At what time are you at the highest point of your jump?
Where does the time you reach the highest point of the jump relate to the start time
and time you hit the water?
At what time interval are you going up?
At what time interval are you going down?
After you have had a chance to anchor the houseboat in deeper water do the following
problems.
Assuming the deck of the houseboat is 10 feet above the surface of the water and you
jump from the deck. Your dive can be modeled by the following equation.
y = -16t2 + 6t + 10
Create a table using appropriate values for x.
When did you hit the water?
According to your table, what is the highest point of your jump and at what time where
you at the highest point?
Is this time half-way between the beginning time and the time you hit the water?
Why or why not?
Find the height at t = 3.75
How can you use this information to find the actual time that you reached the highest
point of your dive?
Cliff diving at Lake Powell is prohibited; however, if you dived off a cliff that is 30 feet
tall, the dive might be modeled by the equation y = -16t2 +4t + 30.
Once again, create a table using appropriate values for x.
What does t = 0 represent?
What does the height at t = 0 represent?
What does “t” refer to at the time ”y” = 0?
Find the height at t = .125 and use this information to find the maximum height and the
time at which it will occur.
Now suppose the crazy person in your group decides to jump off the 50 foot cliff, write
an equation that might model his/her dive.
Construct a graph of a parabola that opens down.
Now construct several horizontal lines intersecting the graph at several locations.
How can the intersection points of each horizontal line with the parabola be used to
find the location of the maximum value of the parabola?
Consider the following.
y = ax2 + bx + c
In the context of our problem, what does y represent?
How would we find the initial height?
What is the initial height?
What does the following statement really mean?
Find x when y = c or in other words solve c = ax2 + bx + c for x.
Now solve the following for x.
ax2 + bx + c = c
What does the average of these two values represent?
What will you find if you evaluate the original quadratic at this average value?