Answer:
maximum width of the doorway = 35.77ft
Explanation:
The detailed calculation and derivation from first principle is as shown in the attachment
Answer:
the maximum width is x= 4√2 ft = 5.656 ft
Explanation:
for the parabola
y= a*x² + b*x + c
where y= height and x= width
an aircraft hangar should be symmetric with respect to the y axis , then
y(-x)=y(x) → a*x² + b*x + c = a*x² - b*x + c →-2*b*x =0 → b=0
it also should be pointing downwards → a is negative
, then the parabola would be
y= c- a*x²
since c= maximum height = 18 ft
then for y=0 , x= 48 ft/2 = 24 ft → 0 = 18 ft - a*(24 ft)² → a= 1/32 ft⁻¹
then
y= 18 ft- 1/32 ft⁻¹ *x²
since the doorway cannot go beyond the parabola , the maximum possible doorway is obtained when the doorway touches the parabola.
then for a height y= 8 ft
8 ft = 18 ft- 1/32 ft⁻¹ *x²
x= 4√2 ft = 5.656 ft
