Question

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway, which is horizontal and 100 m long, is supported by vertical wires attached to the cable, with the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.

A) 24 m
B) 30 m
C) 36 m
D) 40 m

Answer 1

The length of the supporting wire attached to the roadway 18 m from the middle is 42 m.

Step-by-step explanation:

To find the length of a supporting wire attached to the roadway 18 m from the middle, we can consider the shape of the cable as a parabola. The longest wire is 30 m and the shortest wire is 6 m, so we have a difference of 24 m between the longest and shortest wires. Halfway between the shortest and longest wires is the middle of the roadway, where the wire length is 18 m.

We can assume that the shape of the parabola is symmetrical, meaning the difference between the longest wire and the middle wire is the same as the difference between the middle wire and the shortest wire. Therefore, the length of the supporting wire attached to the roadway 18 m from the middle is 18 + 24 = 42 m.