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?


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Answer 1

Step-by-step explanation:

( Attached image ✓ )

Hope it helps you !

Answer 2

Step-by-step explanation:

Let the vertex of the parabola be at the origin and axis be along OY. Then, the equation of the parabola is :

x² =4ay

The coordinates of end A of the arc are (2.5, 10) and it lies on the parabola.

Therefore,

(2.5) ²=4a×10

a= 6.25/40 =5/ 32

Thus, the equation of the parabolic arc is

x² = 5/8 y.

When y=2,

x² = 5/8 ×2

x= √5/2m

Hence, the width of the arc at a height of 2 m from the vertex is 2× √25/2 m

= √5m