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?
Solution:
The origin of the coordinate plane is taken at the vertex of the parabolic reflector in such a way that the axis of the reflector is along the positive y-axis.
This can be diagrammatically represented as
The equation of the parabola is of the form x2 = 4ay (as it is opening upwards).
It can be clearly seen that the parabola passes through the point (5/2, 10).
Hence,
⇒ (5/2)2 = 4a(10)
⇒ a = 25/(4 × 4 × 10) = 5/32
Therefore, the arch is in the form of a parabola whose equation is x2 = (5/8)y
When y = 2,
x2 = (5/8) × 2
x2 = √5/4
x = 5/4
Therefore,
AB = 2 × 1.118 m (approx.)
= 2.236 m (approx.)
NCERT Solutions Class 11 Maths Chapter 11 Exercise ME Question 2
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?
Summary:
When the arch is 2 m from the vertex of the parabola, its width is approximately 2.236 m
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