Question

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. How wide is it 2 m from the vertex of the parabola?

Answer 1

Given, parabolic arch is 10 m high and 5 m wide at the base.

Take origin at the vertex of the parabola in such a way that its vertical axis is along positive y axis.

Assume that the parabolic arch is opening upwards.

The equation of the parabola with vertex at origin and axis along y axis is represented as,

x 2 =4ay

Since parabola passes through point ( 5 2 ,10 ),

( 5 2 ) 2 =4a( 10 ) a= 25 4×4×10 a= 5 32 4a= 5 8

Thus, parabolic equation of the arch is x 2 = 5 8 y.

When y=2 m,

x 2 = 5 8 ×2 x 2 = 5 4 x= 5 4

Now, length of AB is,

Length of AB=2× 5 4 =2×1.118 =2.23 m(approx.)

Thus, the width of parabolic arch is 2.23 m.