Last updated at Dec. 8, 2016 by Teachoo

Transcript

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 = 𝐴𝐵2 = 1002 = 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 = 250024 4a = 6256 a = 𝟔𝟐𝟓𝟐𝟒 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 = 62524 182 = 4 62524 (d – 6) 18 × 18 = 4 62524 (d – 6) 18 × 18 × 244 × 625 = (d – 6) (d – 6) = 18 × 18 × 244 × 625 (d – 6) = 3.11 d = 6 + 3.11 d = 9.11 So, QP = 9.11 m ∴ Length of support is 9.11 m.

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.