A bridge is built in the shape of a parabolic arch. The bridge has a span of 50 meters and a maximum height of 40 meters. How do you find the height of the arch 10 meters from the center?

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Answer 1 · 2016-05-16T06:44:57

$33.6$ meters.

Referring to the highest point as the origin O and the the altitude

from O as the x-axis, the equation of the parabola is $y^2=4ax$

From the data given, the ends of the bridge are at $(40, +-25)$ .

So, $25^2=(4a)(40)$ . This gives a = 125/32.

When, at 10 meters from the center, $y = +-10$ . So, the height

there is $40-x$ , when $y=+-10$ .

From the equation of the parabola, $10^2=(4)(125/32)x$ . So, x =

6.4. And so, the required height $= 40-32/5 = 33.6$ meters.

The graph for the arch is in a befitting frame.

graph{(y-40+0.064x^2)(y)=0[-25 25 -40 40]}