Question

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?

Answer 1

`33.6` meters.

Explanation:

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]}