Question

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

Answer 1

Let $y^2=4ax$ be the equation of parabola where $(a,b),(50,30),(18,y)$ are points on it.

Putting $(50,30)$ in the equation of parabola

$y^2=4ax$, we get,

${30}^2=4a\times 50$

$⟹a=\frac{9}{2}$

Now equation is

$y^2=4^2\times 9x⟹y^2=18x$

Let the length of the wire at $x=18$ be $ym$

$y^2=4\times \frac{9}{2}\times 18⟹y=2\times 9=18m$