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 form the vertex of the parabola?

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 form the vertex of the parabola?

Filo · Accepted Answer

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 positive

y

-axis.

The equation of the parabola is of the form

x^{2} = 4 a y

(as it is opening upwards)
Since, the parabola passes through point

(\frac{5}{2}, 10)

(\frac{5}{2})^{2} = 4 a (10)

\Rightarrow a = \frac{25}{4 \times 4 \times 10} = \frac{5}{32}

So, the equation of arch of parabola is

x^{2} = \frac{5}{8} y

When

y = 2 m

\Rightarrow x^{2} = \frac{5}{4}

\Rightarrow x = \frac{5}{4} m

∴ A B = 2 \times \frac{5}{4} m = 2 \times 1.118 m (a pp ro x) = 2.23 m (a pp ro x)

So, the arch is

2

m from the vertex of the parabola, its width is approximately

2.23

m

Question Text	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 form the vertex of the parabola?
Answer Type	Text solution:1
Upvotes	150

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 form the vertex of the parabola?

Text solutionVerified

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