Unit 5: Quadratic functions and equations. I need help with the Firework display portfolio??
Fireworks Display Portfolio ALGEBRA 2 A: QUADRATIC FUNCTIONS AND EQUATIONS 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 0 h is the initial height is 2 0 ht t h ( ) 16 = − + . • The function for objects that are launched where t is the time in seconds, h is the height in feet at time t, 0 h is the initial height, and 0 v is the initial velocity in feet per second is 2 0 ht t vt ( ) 16 =− + + h0 . Select the link below to access centimeter grid paper for your portfolio. Centimeter Grid Paper 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?
1) Height of local building = 10 feet
2) Intial velocity of a fireworks = 100 ft/sec
3) h(t) = -16t^2 + h
𝐡𝐭𝐭𝐩𝐬://𝐝𝐨𝐜𝐩𝐥𝐚𝐲𝐞𝐫.𝐧𝐞𝐭/𝟐𝟎𝟗𝟓𝟓𝟓𝟗𝟕𝟎-𝐅𝐢𝐫𝐞𝐰𝐨𝐫𝐤𝐬-𝐝𝐢𝐬𝐩𝐥𝐚𝐲-𝐩𝐨𝐫𝐭𝐟𝐨𝐥𝐢𝐨-𝐚𝐧𝐬𝐰𝐞𝐫-𝐤𝐞𝐲.𝐡𝐭𝐦𝐥
Try 175 with a height of 500 feet.
How can you determine the initial velocity and initial height?
you have to change it into normal letters to get to the website
To complete the Firework Display Portfolio, you will need to work through several tasks related to quadratic functions and equations. Here's an explanation of how to approach each task:
Task 1:
- Conduct research to find a local building and estimate its height. Take a picture of the building for reference.
- Use the internet to find different types of fireworks and their initial velocities. Choose one of these values.
Task 2:
1. To determine how long it will take for a tool to fall from the top of the building to the ground, you can use the equation for objects dropped from a height:
- The equation is h(t) = -16t^2 + h0, where h(t) represents the height at time t and h0 represents the initial height.
- Since the tool is dropped, the initial height, h0, is the height of the building. Substitute this value into the equation and solve for t.
2. The given equation is 2ht - t^2 - 16 = 250. To determine if the parabola opens up or down, you can analyze the coefficient of the t^2 term.
- Since the coefficient is negative (-1), the parabola opens downward.
- In the context of this problem, it makes sense that the parabola opens downward because the object represented by the equation is falling due to gravity.
3a. The equation for the firework launched from the top of the building with an initial upward velocity of 150 ft/sec is:
- h(t) = -16t^2 + 150t + h0.
3b. To find when the firework will land if it does not explode, you need to determine the time at which the height, h(t), reaches 0.
- Set h(t) = 0 and solve the resulting quadratic equation for t.
3c. Create a table to show the height from time t = 0 until the firework hits the ground.
- Choose different values for t and calculate the corresponding h(t) using the equation.
3d. The axis of symmetry can be calculated using the formula t = -b/(2a), where a and b are the coefficients of the quadratic equation.
- In this case, the axis of symmetry represents the time at which the firework reaches its maximum height.
- Substitute the values of a and b from the equation and solve for t.
3e. The coordinates of the vertex can be found using the axis of symmetry.
- Substitute the value of t from the axis of symmetry into the equation to find the corresponding h(t) value.
3f. Negative values for t and h(t) do not make sense in this problem because they would imply that the firework is traveling back in time or below the ground.
3g. Graph the situation by plotting points for different values of t and h(t) using the equation.
- Label the axes with a title and scale.
4. To calculate the maximum height of another firework launched from the ground, use the initial velocity and the equation for objects launched.
- Set the equation h(t) = -16t^2 + vt + h0, where v is the initial velocity and h0 is the initial height.
- Substitute the values into the equation and solve for the maximum height using the formula for the vertex.
5. Decide whether you want to launch the third firework from the ground or the building and determine the height at which it will explode and the initial velocity.
- Consider factors like visual aesthetics and safety when making your decision.
- Choose appropriate values for the height and initial velocity.
6. Analyze how the height of the building and the initial velocity of the mortar affect the maximum height reached and the time it takes to reach there.
- Explore the relationship between these variables by varying their values and observing the effects on the maximum height and time.
By following these steps, you will be able to complete the Firework Display Portfolio and gain a better understanding of quadratic functions and equations in the context of setting up a fireworks display.
someone please give me some inital velocitys for fireworks lolol
Did you ever get the answer to this???
surely you have some ideas on some of the sections?!?
A problem like this will not be assigned until after some time has been spent.
Whatcha got so far?