Question

a one way road passes under an overpass in the shape of half an ellipse, 15 ft. high at the center and 20 ft wide. assuming a truck is 12 ft. wide what is the tallest truck that can pass under the overpass?

Answer 1

The tallest truck that can pass under the overpass would be 9 feet in height :)

Answer 2

The answer is 12 feet.

Explanation:

Let the height of the truck be represented by y.

The ellipse has the equation
`(x^(2) )/(10^(2) ) +(y^(2) )/(15^(2) ) =1`

We have to find the y-coordinates when x is equal to 6 (half the width of the road)

So,
`(36)/(100)+(y^(2) )/(225) =1`

Multiplying throughout by 225 to get
`81^(2)+y^(2)=225`

Solving this we get,
`y^(2) =144`

Hence, y = 12

So, the tallest truck that will fit under the pass will be 12 feet tall.