A friend just sent me this question.

It took me a while but I did solve it.

How many of you can solve it?

Find the lengths between the poles.

Melody Apr 13, 2020

#1**+2 **

Wouldn't they be 0 meters apart.... The cable is 10 m above the gound and half the cable is 40 m long. SInce the cable is 10 m above the gound, that means that the cable is 40 m above the ground. If the length of half the cable is 40 m and the cable is 40 m above the ground, wouldn't the cable have to be folded in half? If the cable is folded in half, then the 2 poles are 0 meters apart.

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**Edit:**

Since my previous answer is a total mess, I'll try to clarify.

The problem tells us that the bottom of the cable is 10 m above the gound. Since the poles holding up the cable are 50 m tall, that means that the top of the cable is 50 m above the ground. If we cut the cable in half, there are 40 m on the left and right side. Taking the right side only, the cable is 40 m long. Since the cable is 10 m above the gound, it is 40 m tall. This is the most confusing part that I can't explain well... In order for the cable to be the same length as it is tall, the cable must be right on the pole. For the cable to be on the pole, then the cable must have been folded exactly in half meaning that the distance between the two poles is 0 m.

HELPMEEEEEEEEEEEEE Apr 13, 2020

#5**0 **

You have the right answer, but your explanation is crazy BS!

The cable is 10 m above the gound and half the cable is 40 m long.

SInce the cable is 10 m above the gound, that means that the cable is 40 m above the ground.

If the length of half the cable is 40 m and the cable is 40 m above the ground, wouldn't the cable have to be folded in half

Try proofreading what you write and ...

You may want to limit the Cocopuffs to one bowl...

Guest Apr 13, 2020

#13**0 **

Yes, I believe YOU are correct......the diagram is deceiving !

If you abut the poles (i.e. right next to ecah other with no distance between) , the cable goes from 50 m to 10 m (above the ground) then back to the top of the other pole ..... for a total of 80 m length. SO the distance betwen the poles = 0

(If you start to move the poles apart....the point that is 10 m above the ground will start to rise above 10 m . )

ElectricPavlov
Apr 13, 2020

#7**0 **

Ummmm... this is an Amazon Interview Question? I didn't know they did this before hiring a worker. Or am I just mis-interpeting this.

madyl Apr 13, 2020

#9**+1 **

The mildly embarrassing fact is that I solved it with complicated mathematics.

I got the answer 0 and though I had made a mistake.

I finally looked at it properly and the penny dropped. Doh !!!

Melody Apr 13, 2020

#14**+3 **

Yes, I used co-ordinate geometry.

I let the centre point between the two poles be (0,0)

And I let the bottom of one pole be (-b,0) and the other be (b,0)

This shape is a __catenary__.

The formula for a catenary is

\(\boxed{y=c+acosh(\frac{x}{a})\\ where\\ cosh(x) =\frac{e^x+e^{-x}}{2}}\)

The arclength of this section of catenary is L which is 80m

It can be shown that:

\(L=\displaystyle\int_{-b}^{b}\;\sqrt{1+\left(\frac{dy}{dx}\right)^2}\;dx\)

Put all this together and I ended up getting either nonsense or that b/a=0

It was then that I looked at the question properly and had my Doh! moment.

All suspended ropes, chains etc hang in a catenary.

There are a lot of good youtube clips available if you want to look at them.

Melody
Apr 14, 2020