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

Answer:

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

Step-by-step explanation:

This problem can be represented by an ellipse with a vertical major axis of the standard form:

(x-h)^2/b^2+(y-k)^2/a^2=1, a>b, (h,k)=(x,y) coordinates of center.

center: (0,0) (center line of road)

a=15 ft (height of overpass at center)

a^2=225

b=10 (1/2 the width of the road)

b^2=100

equation of ellipse:

x^2/100+y^2/225=1

The point at which a truck 16 ft wide would touch the overpass would have and x-coordinates �8 ft from center. Its y-coordinate is the answer to given problem.

Plug in x=8 ft in equation to solve for y.

8^2/100+y^2/225=1

y^2/225=1-64/100

y^2=225-225*64/100=81

y=9 ft