Question

Hey guys! I have this portfolio for my Algebra 2 class and I honestly don't know how to do it. Christmas break is coming up fast and no one is able to help me. I have 58 in the class, and need a 70 to pass.

Would any of you guys be interested? If so, whomever is the most helpful will receive fan and medal. Thank you guys in advance!!

Below I have posted the portfolio instructions.

Answer 1

Task 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

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. How long will it take the
tool to fall to the ground?
2. State whether the parabola represented by 2 ht t t ( ) 16 250 =− + 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. 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 launch a third firework. Decide whether you want to launch it from the
ground or from the building. Also, choose 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 conclude 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?

Answer 2

Hi @mathwizzard3 , think you can help?

Answer 3

@Alphabet_Sam ?

Answer 4

Do you have the height of the building and the velocity of the firework that you would like to use?

Answer 5

I think I do. Hold on, let me find it @Alphabet_Sam

Answer 6

Yeh. Khols building- 70ft high
Velocity of fireworks: 175 with a height of 500ft.

Answer 7

175 miles/hour?

Answer 8

Miles, yes

Answer 9

1. Since you're given the displacement that the object will fall (the height of the building) you use the formula:
\[time=\sqrt{2y/g}\]
y is the distance it will fall, in this case 70 ft and g is the acceleration due to gravity, which is 32 ft/(s^2)
\[t=\sqrt{2(70)/32}\]
t=Approx 2.1 sec

2. I am not sure what the equation of the parabola is, I think the formatting got messed up.

3. That's more physics stuff that I'm not too good with, sorry.

Answer 10

Okay, thank you very very much!
Number 2 did get messed up. It's supposed to be: h(t) = -16t^2 + 250t

Answer 11

Okay, so for number 2:
The parabola opens down because the coefficient in front of the t^2 term is negative. This makes sense because it is a graph of an objects flight through the air, which is controlled by gravity, so the object will first go up and then come down.

Answer 12

Okay. Alrighty, I think I understand.

Answer 13

Do you know of anything helpful for 4, 5, and 6? Or are you not sure? @Alphabet_Sam

Answer 14

@ryandane , can you help?

Answer 15

4. You need to convert the speed of the firework from miles/hour to feet/sec so that you can calculate how many feet it will travel in 3 seconds. I'm going to assume you're launching the firework directly upwards because I'm not sure how you would calculate it otherwise (you would have to trace the parabolic path of the firework which is much more complex). I am just going to convert the speed using a calculator because I'm lazy, you can do it by multiplying by the amount of feet in one mile and dividing by the amount of seconds in one hour if you want:
150 mi/hr = 256.667 ft/sec
Then multiply by the 3 seconds: 770 ft

5. How high would you like the firework to go? You need to decide this before starting the problem as well as if you want to launch from the ground or the building.

6. The taller the building and the higher the initial velocity of the firework, the higher the maximum height will be.

Answer 16

Lol I am horrible at math

Answer 17

Okay. I understand :) thank you anyway @ryandane

Answer 18

Thank you @Alphabet_Sam !!! This is awesome. Thank you for all your help :) it means a lot.

Answer 19

Do I have you on instagram ? O.O

Answer 20

Yes :) @ryandane

Answer 21

I didn't help you with 5 yet, if you want me to. You just need to pick how high you want your firework to go and if you want to launch it from the building or from the ground.

Answer 22

Ray lol I thought so :3

Answer 23

Yes please. I need all the help that I can get. Okay.

Answer 24

Lol yes ^.^ it's lee_racheal :) @ryandane

Answer 25

5. Let's say you want the firework to go 1000 feet from the ground. You know the velocity will be 256.667 ft/sec, so you divide 1000 by 256.667 and get 3.9 seconds. If you set the fuse for 3.9 seconds it will explode at 1000 feet.

Also in my calculations for 4 I mistyped, the 150 mi/hr should be 175 mi/hr.

Answer 26

Alrighty, I see. Thank you :) this has been very helpful. @Alphabet_Sam

Answer 27

No problem :)

Answer 28

Alphabet you getting that or what ;)