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

Step-by-step 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* (-40)`

`x^2=160a`

`x=\pm √(160a)`

and it is given,
`2x=100`

`x=50`

`√(160a)=50`

`a=15.625`

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

at
`x=15`

`15^2=-4* 15.625(y-40)`

`y=36.4 ft`