Mathematics
Directions: You are part of a fireworks crew assembling a local fireworks display.
There are two parts to the fireworks platforms: one part is on the ground and the
other part is on top of a building. You are going to graph all of your results on one
coordinate plane. Make sure to label each parabola with its equation. Use the
following equations to assist with this assignment.
The function for objects dropped from a height where t is the time in
seconds, h is the height in feet at time t, and ho is the initial height is
h(t) =-16¢I +11…
The function for objects that are launched where t is the time in seconds, h is
the height in feet at time t, ho is the initial height, and vo is the initial
velocity in feet per second is 11(1) = -16t’ + vault…
Select the link below to access centimeter grid paper for your portfolio.
Centimeter Grid Paper
Ta 5 k 1
First, conduct some research to help you with later portions of this portfolio
assessment.
Find a local building, take a picture of it, and estimate its height.
Use the Internet to find some initial velocities for different types of fireworks.
Use one of these values
Ta 5 k 2
Respond to the following items.
1. While setting up a fireworks display, you have a tool at the top of the
building and need to drop it to a coworker below. How long will it take the
tool to fall to the ground?
2. State whether the parabola represented by 11(1) =-16t2 +250: opens up or
down. Explain why your answer makes sense in the oontext of this problem.
3. One of the fireworks is launched from the top of the building with an initial
upward velocity of 150 ft/sec.
a. What is the equation for this situation?
b. When will the firework land if it does not explode?
c. Make a table for this situation so that it shows the height from time
t = 0 until it hits the ground.
d. Calculate the axis of symmetry.
e. Calculate the coordinates of the vertex.
f. Explain why negative values for t and h(t) do not make sense for this
problem.
9. Graph this situation. Make sure to label your axes with a title and a
scale.
4. Using the initial velocity for a firework that you researched in Task 1,
calculate the maximum height of another firework launched from the ground,
if it is set to explode 3 seconds after launch.
5. You laund’i a third firework. Decide whether you want to launch it from the
ground or from the building. Also, d’ioose a height at which this firework will
explode and an initial velocity for this firework. How long after setting off the
firework should the delay be set?
6. What can you oonclude about how the height of the building and the initial
velocity of the mortar affects the max height and the time it takes to get
there?
S u b m is s i o n
You will submit the following items.
a graph that shows the paths of the three fireworks that were launched
responses to the items in Task 2
results of your research, including the building that you found and initial
velocities for fireworks