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

AI Thread Summary
To determine the tallest truck that can pass under the semi-elliptical overpass, the equation of the upper branch of the ellipse is used: y = 15√(1 - x²/400). Given that the truck is 12 ft wide, it occupies 6 ft on either side of the center, meaning the x-coordinate for the truck's edge is ±6 ft. Plugging x = 6 into the equation yields the height y at that point, which is necessary to find the maximum truck height. The calculation ultimately provides the maximum height for a truck to safely pass under the 15 ft high overpass.
Felidaei
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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!
 
Mathematics news on Phys.org
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 $y(6)$ ...
 

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