Reference no: EM132538047

Suspension Bridges Performance Task

This task is similar to what you did in your formative assessments. The lesson topic that you will be using in this task is the concept of quadratic functions specifically the properties of a parabola. You are given one week to complete this task. Answer each item carefully and SHOW ALL WORK.

Part A. Task context

A state park has two sets of hiking trails. Accessing the second set of trails currently requires wading across a large creek. Park visitors who do not like hiking the trails with wet shoes and clothing have been submitting requests for a suspension bridge over the creek.

One motivated park visitor - probably an engineer - submitted a diagram of a possible suspension bridge.

Figure 1: Suspension Bridge Diagram (Not Drawn to Scale)

In her request, the visitor stated that the main cable creates a parabolic curve once the suspender ropes are connected to the walkway and the weight of the walkway is added.

Part B.

Explain your results in the form of a multimedia presentation describing how your alternate plan is better than the original plan. You must be able to show your model and how much material your plan could save. Present this any way you find most appropriate. You must record your voice while explaining your work.

Question 1. In this design, ropes attach from the main cable to the floor of the walkway every 5 feet between the towers. The ropes form parallel line segments connecting the main cable and the roadway. Figure 1 shows one main cable; but there will actually be 2 parallel main cables.

How many suspender ropes are needed to connect the main cable to the floor of the walkway between the two towers?
Support your answer.

Question 2. Maria says the equation y= 1/200x²+5 is the only equation that can be used to represent the main cables in Figure 1. Describe where Maria had to placed the vertex of the parabola in order for this equation to be true and the coordinates of the tops of the towers.

Question 3. Do you agree or disagree with Maria's claim in question 2 that there is only one equation that can represent the main cable? Support your decision.

Question 4. After analyzing the proposed design, park officials conclude that the expenses associated with the park visitor's design is excessive. The distance between the towers must equal 200 feet. Show how decreasing the height at which the main cable is connected to both towers can reduce the expense of building the bridge. Based on your research, what other features that might need changing if you change the height of the towers?

Question 5. The main cable must be a parabolic curve and there must be a minimum of 5 feet between the walkway and the main cable. At what height do you recommend connecting the main cable to each tower in order to minimize the amount of rope needed to connect the main cable to the roadway?

Sketch a new design and label the height at which the main cable connects to the towers.
Write an equation for the main cable and describe where the origin is located for your equation to be true.

Question 6. Show that your design in question 5 reduces the total length of rope that is necessary to connect the main cable to the roadway.

Question 7. Explain your results in the form of a multimedia presentation describing how your alternate plan is better than the original plan. You must be able to show your model and how much material your plan could save. Present this any way you find most appropriate. You must record your voice while explaining your work.

Closure - Reflection
How were you able to use your self-management skills on this task? Did you do the task in a timely manner or did you just did all the work on the last day? How do you plan to improve this skill next school year?