Can all the trucks pass in this tunnel without exceeding the red line indicated in the figure?

The heights mentioned is from ground to the top of the trucks.

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## Comments

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TopNewestDo you mean the red lines indicated? Or there are some other blue lines that is not shown?

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Sorry I meant the read line.

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The truck with the largest cross-section diagonal is the one with the greatest dimensions; namely, 2.4m x 3.3m. We have that \(\sqrt{2.4^2+3.3^2}\approx 4.08\); but since the semi-cylinder can only fit up to 4 meters diagonally, not all the trucks can fit.

I am assuming that the truck must occupy one half of the cylinder or less, therefore following driving laws.

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have four lanes semi trucks go on the 2 enter lanes even tho its not safe

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is it one way or two day road ?

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one way

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ALL trucks can pass through the tunnel .Any truck with width 2.4 and height not greater than 3.815... can pass through the tunnel.

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\(=\quad \{ (l,\quad h):\quad \frac { { l }^{ 2 } }{ 4 } +{ h }^{ 2 }\le { R }^{ 2 },\quad 2\le l\le 2.40,\quad 3.10\le h\le 3.30\} \)

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i assumed that the truck shouldn't exceed the line halving the tunnel width ,or the tunnel radius . in this case if the maximum height is 3.3 m ,then the maximum width should be 3.3 m also ,because the cross section of the tunnel is a half circle ,so yes all the trucks can pass the tunnel .

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Is the height of the truck tires significant?

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The height of the truck mentioned includes the height of the truck. Sorry the picture should be modified so the height line should go all the way to the ground.

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All I could do is frame both L and h

\(2 \leq L \leq 2.40\)

\(3.10 \leq h \leq 3.30\)

What should I do next?

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Distance from the center to the circumference stays the same. So, (l/2)^2 + h^2 <= r^2 where r is the radius. I can't figure out the blue line in your picture.

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I meant red line

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