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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________?

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________?

Grade:12th pass

2 Answers

Sunil Kumar
askIITians Faculty 183 Points
7 years ago

1027_96661_parabola.JPG

Thanks & Regards
Sunil Kumar, 
askIITians Faculty
M.Sc., IIT Kharagpur

ATHARVA_12
13 Points
7 months 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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