SOLUTION: Hi, I hope you are doing fine. Can you help me? The minimum width of a two-way road in the Philippines is 6.10 meters. A 500- meter tunnel is to be constructed so that its cross

Question 1185202: Hi, I hope you are doing fine. Can you help me?
The minimum width of a two-way road in the Philippines is 6.10 meters. A 500- meter tunnel is to be constructed so that its cross- section is a semi- elliptical. If the height of the tunnel should be 8 meters, what should be the maximum height of cars entering the tunnel? ( use a 0.5 meter clearance from the side of the tunnel.)
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The half axis in the x direction is 6.10/2 = 3.05m; the half axis in the y direction is 8m. The equation (assuming for simplicity the center of the ellipse at the level of the road and in the middle of the tunnel) is

Solving for y,

Plug in x=2.55 to allow the 0.5m clearance from the wall of the tunnel and evaluate.

My answer: 4.389m

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