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Chapter 11 Class 11 Conic Sections
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Misc 3 - The cable of a uniformly loaded suspension bridge hangs - Parabola - Beam problem

Misc 3 - Chapter 11 Class 11 Conic Sections - Part 2
Misc 3 - Chapter 11 Class 11 Conic Sections - Part 3 Misc 3 - Chapter 11 Class 11 Conic Sections - Part 4 Misc 3 - Chapter 11 Class 11 Conic Sections - Part 5 Misc 3 - Chapter 11 Class 11 Conic Sections - Part 6

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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.

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.