Question

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

Answer 1

The length of vertical cube is 29 / 4.

Step-by-step explanation:

Let us assume that lowest point of cable as origin and equation of parabola will be x^2  = 4 a.y  

Given, tower of bridge is 30 meters above the road-way and lowest point is 5 meters above the road.

Then in equation y-coordinate of top of tower is 25 meters and x-coordinate is 100 meters.

From equation we get 100^2   = 4 a(25) ⟹ a = 100

Now,length of the vertical supporting cable 30 metres from the centre is given by y+5 where y is given by 30^2  = 4 (100) (y)

⟹ y =   9/4

Then vertical length of cable is 5 +  9 / 4   =   29  / 4

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