Q. 13

# The towers of bridge, hung in the form of a parabola, have their tops 30 m above the roadway, and are 200 m apart. If the cable is 5 m above the roadway at the center of the bridge, find the length of the vertical supporting cable, 30 m from the center.

Given: Top of the towers are 30 m above the roadway and are 200 m apart. Cable is 5 m above the roadway at center.

Need to find: Length of the vertical supporting cable, 30 m from the center. A and B are the top of the towers. AE and BF are the height of the towers. H is the center of the bridge. HI is the 5 m above from the roadway.

Let, the equation of the parabola be: x2 = 4a(y – b)

Here b = 5. So, x2 = 4a(y – 5)

Here, AB = 200 m and BF = 30 m.

So, the coordinate of the point B is (100, 30)

The point is on the parabola.

Hence, x2 = 4a(y – 5)

10000 = 4a (30 – 5)

10000 = 4a x 25

a = 100

Now we need to find, the length of the vertical supporting cable, 30 m from the center.

The x-coordinate of the point, 30 m from the center, is 30.

So, 30 x 30 = 4a (y – 5)

900 = 400 (y – 5)

y – 5 = y = So, the length of the vertical supporting cable is m = 7.25 m

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Interactive Quiz on Equation of Parabola41 mins  Lecture on Equation of Parabola59 mins  Applications of +I and -I41 mins  Interactive Quiz on Algae32 mins  Features, similarities and dissimilarities between bryophytes and pteridophytes51 mins  Dicot and Monocot root35 mins  Interactive Quiz on Plant Tissues52 mins  How to correlate the features of multicellular algae and protists57 mins  Pseudo Force52 mins  Modifications of stem49 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 