An arch is in the form of a parabola with its axis vertical. The arc is 10m high and 5m wide at the base. How wide is it 2m from the vertex of the parabola?

Explanation

From the figure, AB is base and height is 12 m.
Consider parabola `x^(2)=4ay`.
From the figure, point (3,12) lies on the parabola.
`:." "9=4xxaxx12`
`:." "4a=(3)/(4)`

Therefore, equation of parabola is `x^(2)=(3)/(4)y`
When `y=6,x^(2)=(9)/(2)`.
`:.` Width `2xx(3)/(sqrt(2))=3sqrt(2)m`