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Question 590887: a one-way road passes under an overpass in the shape of half and ellipse, 15ft high at the center and 20ft wide. Assuming a truck is 16ft wide, what is the tallest truck that can pass under the overpass?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! a one-way road passes under an overpass in the shape of half and ellipse, 15ft high at the center and 20ft wide. Assuming a truck is 16ft wide, what is the tallest truck that can pass under the overpass?
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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
ans:
The tallest truck that can pass under the overpass would be 9 feet in height
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