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Grade 12th passAnalytical Geometry

a telegraphic wire suspended between two poles of height 15mt is in the shape of a parabola.the distance between the poles is 20mt and maximum sag of the cable wire is 4mt.then the height of cable at a distance of 5mt from one end is________?

Ashish Reddy

12 Years agoGrade 12th pass

2 Answers

Sunil Kumar

12 Years ago

Thanks & Regards

Sunil Kumar,

askIITians Faculty

M.Sc., IIT Kharagpur

ATHARVA_12

5 Years ago

Let Vertex be (0,0) and let the parabola be

x²=4ay..... so by symmetry when x=10m then y=4m(maximum saag)

then,on substituting x and y we get

100=16a so 4a=25

hence,the eq of parabola is x²=25y as(4a=25.)

then at distance x=5 then let point on parabola be(5,w) then

5²=25y …... so y=1

Now, as the sag is 4m and height of towers is 15m,So the the lowaset point of the wire is 11m above the ground

hence,the height of the point 5m away from one end is..
11+y-->11+1=>12m

so height of the point at a distance 5m from one end is 12m.

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