Question

TASK: You are tasked with analyzing a design that has been drawn for a bridge over an existing two-lane road. The arch over the road is in the shape of a half-ellipse that is 40 feet wide at the base of the arch and it is 15 feet tall at the center of the arch. The bridge must have a 13-foot clearance for vehicles on the road. The 22-foot-wide road is centered directly beneath the highest point of the arch. e. Will the current bridge design allow 13-foot-tall vehicles to pass on the road beneath it? Explain the reasoning for your answer. Yes! Explain. (Then, go to part f.) No. Explain. (Then, go to part g.)

Answer 1

Given

Shape of bridge is half ellipse

Width of road = 22ft

height of bridge = 15ft

Find

Will a 13 ft vehicle can pass through bridge

Explaination

First we have to find the value of h1 or h2 if its value is more than 13 then the vehicle can pass through it

Equation of ellipse

`(x^2)/(20^2)+(y^2)/(15^2)=1`

Points E and F are lying on the Ellipse so they must satisfy this equation

`\begin{gathered} (11^2)/(20^2)+(h^2)/(15^2)=1 \\ ((h)/(15))^2=1-(121)/(400) \\ ((h)/(15))^2=(279)/(400) \\ (h)/(15)=(16.70)/(20) \\ h=12.525ft(approx) \end{gathered}`

Final Answer

No, 13 ft vehicles would not be able to pass beneath the bridge