Misc 3
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, 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.
Cable is always facing upwards with the axis vertical
Since, the axis is positive y-axis,
its equation is
x2 = 4ay
First, we find coordinates of point B
Given length of cable = 100 m
Hence, AB = 100 m
So, BC = 2 = 100 2 = 50 m
Also,
DB = 30 6 = 24 m
Hence point B is B (50, 24)
Now,
Since point B(50, 24) lies on the parabola
Putting x = 50, y = 24 in equation of parabola
x2 = 4ay
(50)2 = 4a (24)
2500 = 4a 24
4a 24 = 2500
4a = 2500 24
4a = 625 6
a =
Now, we need to length of a supporting wire attached to the roadway 18 m from the middle
Hence OR = 18 m,
We need to find QP
Let QP = d
So, QR = QP 6 = d 6
So, coordinates of point Q is Q(18, d 6)
So, coordinates of point Q is Q(18, d 6)
Since point Q lies on parabola
it will satisfy the equation of parabola
Equation of parabola is
x2 = 4ay
Putting x = 18 & y = d 6 & a = 625 24
182 = 4 625 24 (d 6)
18 18 = 4 625 24 (d 6)
18 18 24 4 625 = (d 6)
(d 6) = 18 18 24 4 625
(d 6) = 3.11
d = 6 + 3.11
d = 9.11
So, QP = 9.11 m
Length of support is 9.11 m.

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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