Question

An arch for a bridge ovre ahighway is in the form of half of an ellipse .the top ofthe arch is 6m abve the ground level(the major axis).the high way has four label eahc 3.6 m wide center a center safety strip 2.4m wide ,and two sides strip2.4m wide and two sieds strip each 1.2m wide .what should the span of a bridge be .(the length of its major axis) if the height 8.4m from the center is tobe 3.9m

Answer 1

Explanation:

The height of the arch is given as 8.4 meters from the center, and the desired height at this point is 3.9 meters. Let's call the span of the bridge s, which is the length of the major axis of the ellipse.

We can use the formula for the vertical distance between the foci of an ellipse and a point on the ellipse:

[(distance between foci)^2 - (distance from point to major axis)^2]^(1/2) = distance from point to minor axis

In this case, the distance between the foci is 4.2 meters (half of the desired height of the arch), and the distance from the point to the major axis is 8.4 meters. Therefore, we can substitute these values into the formula as follows:

[(4.2)^2 - (8.4)^2]^(1/2) = 3.9

Solving for s, we find that s = 18.8 meters.

Therefore, the span of the bridge should be 18.8 meters in order to have a height of 3.9 meters at a point 8.4 meters from the center.

I hope this helps! Let me know if you have any further questions.