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 :
A parabolic reflector is 5 cm deep and its diameter is 20 cm. How far is its focus from the vertex?RS Aggarwal - Mathematics
A beam is supported at its ends by supports which are 12 m apart. Since the load is concentrated at its center, there is a deflection of 3 cm at the center, and the deflected beam is in the shape of a parabola. How far from the center is the deflection 1 cm?RS Aggarwal - Mathematics