How do i calculate this? is there a formula? a suspension bridge with weight uniformly

Height of cables = 23.75 meters

Step-by-step explanation:

We are given that the road is suspended from twin towers whose cables are parabolic in shape.

For this situation, imagine a graph where the x-axis represent the road surface and the point (0,0) represents the point that is on the road surface midway between the two towers.

Then draw a parabola having vertex at (0,0) and curving upwards on either side of the vertex at a distance of or , and y at 95.

We know that the equation of a parabola is in the form and here it passes through the point .

So new equation for parabola would be .

Now we have to find the height of the cable when .

y = 23.75 meters

23.75 meters

Step-by-step explanation:

If we assume that the origin of the coordinate axis is in the vertex of the parabola. Then the function will have the following form:

We know that when the height of the cables is equal to 95 then the horizontal distance is 600 or -600.

Thus:

Then the equation is:

Finally the height of the cables at a point 300 meters from the center is:

The height of the tree is 14.85 m

Step-by-step explanation:

The length of the shadow cast by the tree = 25 m

The length of the shadow cast by the signpost = 6 m

The height of the signpost = 3.5 m

Therefore, by similar triangles, we have;

Let θ, represent the angle formed by the line extending a line from the tip of the shadow, to the tip of the object and let x represent the height of the tree, we have

Tan(θ) = Opposite/Adjacent = Height of the object/(The length of the shadow)

∴ Tan(θ) = 3.5/6 = x/25

x = 25 × 3.5/6 = 14.58

The height of the tree = x = 14.85 m