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 wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find t

Options

A. 9.11 m
B. 9.01 m
C. 9 m
D. None of these

Answer

A

Explanation

Here, wires are vertical let equation of the parabola be in the from x^(2)=4ay focus is at the middle of the cable and shortest and longest vertical supports are are 6m and m and roadway in 100 m long.clearly, the coordinates of Q(50,24) will satisfy eq. (i).`
`therefore (50)^(2)=4ax24rArr2500=96arArra=2500/96`
hence, from eq. (i),`x^(2)=4x2500/96yrArrx^(2)=2500/24y` let pr=k m then, point p (18,k) will satisfy the equation of parabola. `therefore(18)^(2)=2500/24xk`
`rArr324=2500/24k`
`rArr k=(324x24)/(2500)=(324x6)/(625)=(1944)/(625)`
`rArr k=3.11`
`therefore` required length=6+k=6+3.11=9.11 m (approx.)