Truck Height Limit for Ellipse Overpass: 40ft Wide, 15ft High

In summary, the purpose of having a truck height limit for an ellipse overpass is to prevent collisions and ensure road safety. The specific dimensions for the limit are 40 feet wide and 15 feet high, determined through calculations and simulations by engineers and transportation officials. If a truck exceeds the limit, it may result in damage and potential fines. While there are typically no exemptions, exceptions may be granted for emergency or construction purposes on a case-by-case basis.
  • #1
Felidaei
1
0
The question asks, "A one-way road has an overpass in the form of a semi-ellipse, 15 ft high at the center, and 40 ft wide. Assuming a truck is 12 ft wide, what is the tallest truck that can pass under the overpass?"

I don't think this is a super complicated question yet it proves to be too confusing for my brain >_<
Any kind of help would be appreciated, thank you!
 
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  • #2
Upper branch of the ellipse $\dfrac{x^2}{20^2}+\dfrac{y^2}{15^2}=1$ is ...

$y=15\sqrt{1-\dfrac{x^2}{20^2}}$

Now determine $y(6)$ ...
 

1. What is the purpose of a truck height limit for the ellipse overpass?

The truck height limit for the ellipse overpass is in place to ensure the safety of both the drivers and the structure itself. It prevents trucks that are too tall from attempting to pass through the overpass and potentially causing damage or accidents.

2. How is the truck height limit determined for the ellipse overpass?

The truck height limit for the ellipse overpass is determined by the height of the overpass itself. In this case, the overpass is 15ft high, so any trucks taller than that will not be able to safely pass through.

3. Are there any exceptions to the 40ft wide, 15ft high truck height limit for the ellipse overpass?

There may be certain exceptions to the truck height limit for the ellipse overpass, such as emergency vehicles or oversized trucks with special permits. However, these exceptions are typically closely monitored and regulated.

4. What happens if a truck that exceeds the height limit attempts to pass through the ellipse overpass?

If a truck that exceeds the height limit attempts to pass through the ellipse overpass, it may cause damage to the overpass and/or the truck itself. This can result in traffic delays, costly repairs, and potential safety hazards.

5. Is there a penalty for violating the truck height limit for the ellipse overpass?

Yes, there may be penalties for violating the truck height limit for the ellipse overpass. This can include fines, points on a driver's license, and potentially even legal consequences if the violation results in accidents or damage. It is important for drivers to adhere to all posted height limits for their own safety and the safety of others.

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