Question

An arch is in the shape of a parabola with its vertex at the top. It has a span of 100 feet and a maximum height of 40 feet. Find the equation of the parabola, and determine the height of the arch 15 feet from the center of the base of the arch.

Answer 1

Answer:36.4 ft

Explanation:

Given

Span of Parabola $L=100 ft$

Maximum height $h=40$

suppose Parabola is of type

$(x-x_0)^2=-4a(y-y_0)$

where $x_0,y_0$ is the center of parabola

$x_0=0, y_0=40$

$x^2=-4a(y-40)$

at $y=0$

$x^2=-4a\times (-40)$

$x^2=160a$

$x=\pm \sqrt{160a}$

and it is given, $2x=100$

$x=50$

$\sqrt{160a}=50$

$a=15.625$

thus $x^2=-4a(y-40)$

at $x=15$

$15^2=-4\times 15.625(y-40)$

$y=36.4 ft$