As shown in the figure, a plane rectangular coordinate system is established.
Let AB and y axis intersect at h,
AB = 36
∴AH=BH=36/2= 18
According to the question:
OH=7 CH=9
∴OC=9+7= 16
Let the analytical formula of parabola be:
y=ax^2+k
Vertex C(0, 16)
∴ parabola y = ax 2+16
Substitution point (18,7)
∴7= 18× 18a+ 16
∴7=324a+ 16
∴324a=-9
∴a=-9/324=- 1/36
∴ parabola: y =- 1/36x 2+ 16
When y=0,-1/36x2+ 16 = 0.
∴- 1/36x^2=- 16
∴x^2= 16×36=576
∴x= 24
∴E(24,0),D(-24,0)
∴OE=OD=24
∴DE=OD+OE=24+24=48
As this is a practical problem, ∴DE=48m.