Question

The tower of bridge hang in
the form of parabola have
there top 30 m above the
road way and are 200 m
apart. If the cabel is 5m
above the road way at the
centre of bridge. Find the
length of vertical supporting
cabel from the centre.​

Answer 1

Answer:

Step-by-step explanation:

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