Fireworks Portfolio

Please help, This question has been resubmitted already, with incomplete answers.

Thank you very much in advance!

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 graph 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

h is the initial height

h ( t)=-16t^2+h

The function ( for objects that are launched where t is the time in seconds, h is the height in feet at time t, h is the initial height, and v is the initial velocity in feet per second ) -- is

h(t)=16t^2+vt+h

Use Centimeter Grid Paper

Task 1

First, conduct some research to help you with later portions of this portfolio assessment.

Find a local building and estimate its height. How tall do you think the building is?

Use the Internet to find some initial velocities for different types of fireworks. What are some of the initial velocities that you found?

Task 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.

a. How long will it take the tool to fall to the ground? use equation

h(t)=-16t^2+h

(hint -For the buildings height, use the height of the building that you estimated in Task 1.)

b. Draw a graph that represents the path of this tool falling to the ground. Be sure to label your axes with a title and a scale. Your graph should show the height of the tool, h, after t seconds have passed. Label this line Tool.

2. State whether the parabola represented by h(t)=-16t^2+250t opens up or down. Explain why your answer makes sense in the context 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.

g. On the same coordinate plane from #1, draw a graph that represents the path of this firework. Make sure that your graph is labeled appropriately. Label this graph Firework #1.

4. Choose an initial velocity for a firework based on your research from Task 1

a. Write an equation that represents the path of a firework that is launched from the ground with the initial velocity that you chose.

b. Suppose this firework is set to explode 3 seconds after it is launched. At what height will this firework be when it explodes?

c. On the same coordinate plane that you have been using, draw a graph that represents the path of this firework. Mark your graph to indicate the point at which the firework will explode. Label this graph Firework #2.

5. You launch a third firework. Decide whether you want to launch it from the ground or from the roof of the building. Also, choose a height at which this firework will explode and an initial velocity for this firework.

a. How long after setting off the firework should the delay be set?

b. On the same coordinate plane that you have been using, draw a graph that represents the path of this firework. Mark your graph to indicate the point at which the firework will explode. Label this graph Firework #3.

6. What can you conclude about how the height of the building and the initial velocity of the item launched affect the maximum height and the time it takes to get there?