Question

b) the restaurant plans to allow older children to bungee jump from the arch. upon hearing of your teams expertise, the manager hires you to calculate the maximum stretch of a bungee cord that would keep the children safe. the jumping location will be 5 horizontal feet away from the archs axis of symmetry. what is the maximum length in which the bungee cord could stretch yet prevent the restaurant from any lawsuits? draw a diagram. how high is the arch 5 feet away from the middle?

Explanation:

Step1: Assume arch equation

Assume the arch is a parabola of the form \(y = ax^{2}+bx + c\). If the arch is symmetric about the y - axis (axis of symmetry \(x = 0\)), then \(b = 0\), so \(y=ax^{2}+c\). We need more information about the arch (such as its maximum height and width) to fully define the equation. But if we assume the general form and we know we want to find \(y\) when \(x = 5\).

Step2: Substitute \(x = 5\) into equation

If \(y=ax^{2}+c\), then when \(x = 5\), \(y=a\times5^{2}+c=25a + c\). Without knowing the values of \(a\) and \(c\) (which would come from the overall description of the arch's shape and dimensions), we can't get a numerical answer. But the process is to use the equation of the arch's curve.

Answer:

We need more information about the arch (such as its maximum height and width to determine the values of \(a\) and \(c\) in the parabola equation \(y = ax^{2}+c\)) to calculate the height of the arch 5 feet away from the middle.