Question

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 verticle wires attached to the cable, the longest wire being $30m$ and the shortest being $6m$. The length of a supporting wire attached to the road way $18m$ from its middle

• A. $10m$
• B. $9.11m$
• C. $9m$
• D. $11m$

Answer 1

The correct option is B $9.11m$

Let equation of parabola be $y={ax}^2+bx+c$ at $x=0$, $y=6$

at $x=50$, $y=30$

$\Rightarrow$ $C=6$

$30=a{\left(50\right)}^2+b\left(50\right)+6$

$\Rightarrow 30=2500a+50b+6$

$\Rightarrow 2500a+50b=24⟶\left(1\right)$

at $x=-50$, $y=30$

$\Rightarrow 2500a-50b=24$

$\Rightarrow 5000a=48$

$\Rightarrow a=48/5000$

$\Rightarrow b=0$

$\therefore$ at $x=18$, $y=\frac{48}{5000}\times {\left(18\right)}^2+6$

$\Rightarrow y=9.11m$ [B]