Question

How far apart are poles which is connected by cable of 80m long to two poles ,and 50 height each pole and distance between cable to surface is 10m

Answer 1

The distance between the poles which is connected by cable of 80m long to two poles ,and 50 height each pole and distance between cable to surface is 10m is given as follows.

Consider the attached figure, while going through the following steps.

Considering the right half of the diagram, we have,

Considering the height of the poles be 50 m and the distance between the cable to the surface is 10 m, we have,

$y=a cosh(\dfrac{x}{a})$

y = 50 m

a = 10 m

$50=10 cosh(\dfrac{x}{10})$

$5 = cosh(\dfrac{x}{10})$

applying cosh^{-1} on both sides, we get,

$cosh^{-1}5 = \dfrac{x}{10}$

2.29 = x / 10

x = 23

Hence the distance between the poles is 2 × 23 = 46m.

Answer 2

Answer:

0.0 m

Step-by-step explanation:

The cable is 80m long. If the poles are 80 m apart, the chain would need to be stretched horizontally. As the poles are brought closer together, the chain hangs and its midpoint is closer to the ground. The minimum distance that the chain can be above the ground is given when the poles are brought to the same spot and the chain hangs directly down (folded in half). As the chain is 80m long, half the length is 40m. This would have the middle of the chain be 10m off the ground. Any separation between the poles would have the chain hanging higher off the ground.