"A bridge is to be constructed across a river that is 200 feet wide. The arch of the bridge is to be semielliptical and must be constructed so that a ship 40 feet wide and 30 feet high can pass safely through the arch with a horizontal clearance of 5 foot on each side. Find the equation for the arch and approximate the height of the arch in the middle of the bridge."
2007-12-03 10:25:52 · 1 answers · asked by Mr. R 2 in Science & Mathematics ➔ Mathematics
I think ellipse passes through this point: (25, 30)
2007-12-05 05:56:49 · update #1
Let the ellipse be centered at the origin, major axis along the x axis. The equation of the ellipse takes on this form:
x^2/a^2 + y^2/b^2 = 1
a = 200/2 = 100
Given that the ellipse passes through this point: (20, 35)
20^2/100^2 + 35^2/b^2 = 1
35^2/b^2 = 1 - 1/25
35^2 = b^2(24/25)
b = 175/(2√6)
The equation becomes:
x^2/100^2 + y^2/(30625/24) = 1
Height of the arch in the middle of the bridge:
x = 0 ===>
y = √(30625/24) = 35.722ft
2007-12-04 14:39:47 · answer #1 · answered by jsardi56 7 · 0⤊ 0⤋