An arch is

The origin of the coordinate plane is taken at the vertex of the arch in such a way that its vertical axis is along the negative y –axis.

This can be diagrammatically represented as

The equation of the parabola is of the form x² = -4ay (as it is opening downwards).

It is given that at base arch is 10m high and 5m wide.

Therefore, y = -10 and x = 5/2 from the figure above.

It can be clearly seen that the parabola passes through point

Therefore, the arch is in the form of a parabola whose equation is

We need to find width, when height = 2m.

Therefore, to find x, when y = -2.

When, y = -2,

Hence, when the arch is 2m from the vertex of the parabola, its width is approximately 2.23m.