Given an arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base.

Now from the figure,

It is clear that Coordinate of B is (5/2, 10)

and equation of the parabola is x² = 4ay ..............1

Let the coordinate of point D is (b, 2) where CD = 2b

Now since B lies on the parabola, then from equation 1, we get

(5/2)² = 4a* 10

=> 25/4 = 4a*10

=> 4a = 25/(4*10)

=> 4a = 25/40

=> 4a = 5/8

Now again fron equation 1, we get

x² = 5y/8 ............2

Again D also lies on the parabola, the from equation 2,

      b² = (5*2)/8

=> b² = 10/8

=> b² = 5/4

=> b = √(5/4)

=> b = √5/2

=> b= 2.236/2

=> b= 1.118

So AB = 2*1.118

=> AB = 2.236  (approximately)

Hense when the arc is 2 m from the vertex of the parabola, its width is 2.236 m approximately.