|
Question 976252: a one-way road passes under an overpass in the shape of half and ellipse, 30ft high at the center and 20ft wide. Assuming a truck is 12ft 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, 30ft high at the center and 20ft wide. Assuming a truck is 12ft wide, what is the tallest truck that can pass under the overpass?
***
Ellipse has a vertical major axis
Its basic form of equation:
x^2/b^2+y^2/a^2=1
For given problem:
a=30
b=10
equation: x^2/10^2+y^2/30^2=1
=x^2/100+y^2/900=1
coordinates of point at which a 12 ft wide truck would reach the overpass=(6,y)
plug in x-coordinate and solve for y
y^2/900=1-x^2/100=1-36/100=54/100
y^2=9*54=486
y=√486≈22
what is the tallest truck that can pass? < 22 ft
|
|
|
| |
