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Q.

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The road way which is horizontal and 100m long is supported by vertical wires, attached to the cable, the longest wire being 30m and the shortest being 6m. The length of supporting wire attached to the road way 18m from its middle is equal to

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answer is 9.

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Detailed Solution

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Parabola is $x^{2} = 4 a y .$
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$2500 = 4 a (24) \Rightarrow 4 a = \frac{625}{6}$
$∴ x^{2} = \frac{625}{6} y$ point
$Q (18, y)$ lies on $x^{2} = 4 a y \Rightarrow 18^{2} = \frac{625}{6} y \Rightarrow 3.11 m$ length of supports wire is attached $= 6 + 3.11 \Rightarrow 9.11 m$

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