Question

An engineer designs a cable of a suspension bridge that hangs in the form of a parabola, the towers supporting the cable are 360 meters apart. The cable passes over the supporting towers at a height of 80 meters above the roadway and the lowest point of the cable is 10 meters above the roadway. Find the lengths of the vertical supporting rods from the cable to the roadway at intervals 60 meters from the center of the bridge to a supporting tower.

Answer 1

Step-by-step explanation:

.....,.........................

Answer 2

Given:

Distance between the towers = 360m

Height of the towers = 80m

Height of the lowest point of the cable = 10m

To Find:

The lengths of the vertical supporting rods from the cable to the roadway at intervals 60 meters from the center of the bridge to a supporting tower.

Solution:

Set up the parabola with its vertex at (0,10). The equation is=

$y = ax^2 + 10$

Since the 80m towers are 180 meters from the center,

⇒ $a X 180^2 + 10 = 80$     - (1)

so a = 7/3240

Thus the equation is

$y = \frac{7}{3240} x^2 + 10$             - (2)

 

Lengths of the cable = y coordinate of y at x = ± 60,120

Putting x = 60 in equation (2), we get:

y = 7.77 + 10 = 17.77

Putting x = 120 in equation (2), we get:

y = 31.11 + 10 = 41.11

Hence, the lengths of the vertical supporting rods from the cable to the roadway are 17.77 m and 41.11 m respectively.