Question

An arc in the shape of parabola measures 6 m across the base and its vertex is 2.5 m above the base. determine he lenght of the beam parallel to the base and 2m above it.

Answer 1

if we set the center of the base at (0,0) then the parabola is modeled by the equation

y = 5/2 - 5/18 x^2

Solve for x when y=2, and the beam has length 2x.

Answer 2

use this formula to solve the x when y=h(1-x^2/a^2)
answer = 2.68 m

Answer 3

Use squared property of parabola
(x sub 1)^2 / (y sub 1)^2 = (x sub 2)^2 / (y sub 2)^2
where xsub1 = 3, ysub1 = 2.5, ysub2 = 2
Not sure if xsub2 = length of beam
or xsub2 = length of beam ÷ 2

But if xsub2 = length of beam, xsub2 = 2.68m (which is the answer in the answer key)

Answer 4

CORRECTION!! Let vertex be at (0,0)
Using squared property of parabola
(x sub 1)^2 / (y sub 1)^2 = (x sub 2)^2 / (y sub 2)^2
where x and y are measured from the vertex
xsub1 = 6m, ysub1 = 2.5m, ysub2 = 0.5m, and
xsub2 = length of beam 2 m from the base
(6)^2 / 2.5 = (x sub 2)^2 / 0.5
xsub2 = 2.68
Therefore, length of beam 2 m from the base = 2.68m