1. ## How High?

There are two vertical poles, one 3m high and one 2m high. There is a rope from the top of each to the bottom of the other.
How far above the ground do the two ropes cross?

2. ## Re: How High?

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">1.2 metres above the ground.</span hide>

3. ## Re: How High?

Good puzzle John... and I get the same result as Hans.

Alan

4. ## Re: How High?

This is very similar to my <post#=520,475>post 520,475</post#> from 2005. Luckily your answer concurs but it was stipulated in the answer that the alley would have had to be 1 metre wide!!!!!!

Surely if the distance the poles are apart varies then the cross over point will vary <img src=/S/shrug.gif border=0 alt=shrug width=39 height=15>

5. ## Re: How High?

In your puzzle, the lengths of the ladders were given, here the height of their end points above the ground. In this puzzle, the distance between the walls falls out of the equation, so the height of the point of intersection is independent of that distance.

6. ## Re: How High?

Gotcha, I am just scribbling on my scratch pad and it has come apparent <img src=/S/blush.gif border=0 alt=blush width=15 height=15>

7. ## Re: How High?

This came from The Age newspaper, which had a two page spread of maths puzzles last week. This was number 58 out of 60.

I agree with the answer given by you and Hans (and so does The Age)

If you generalize to poles of height a and b the answer is <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">(a*/(a+</span hide>

8. ## Re: How High?

Thanks for this John.
This works exactly like resistors in parallel; but I am stumped in trying to develop a descriptive analogy.

9. ## Re: How High?

Thanks Don for pointing out the similarity with resistors in parallel.

I had not noticed, as I always think of that formula as 1/R = 1/R1 + 1/R2

So , is there some parallel between the two apparently unrelated situations that explains the same formula?

10. ## Re: How High?

I think that I have grasped the analogy.

If pole A is infinitely high, the ropes will intersect at the tip of pole B; similarly with two resistors in parallel if resistor A has infinite resistance, the network resistance is that of resistor B.

If pole A has a height of zero, the ropes will intersect at zero height; similarly with two resistors in parallel if resistor A has zero resistance, the network has zero resistance.

11. ## Re: How High?

Interesting. I wonder what the geometrical poles analogy is for two resistors in series? <img src=/S/thinks.gif border=0 alt=thinks width=15 height=15>

Alan

12. ## Re: How High?

Place one pole on top of the other? (You can simply add the lengths.)

13. ## Re: How High?

I thought of that, but then thought there must be something "cooler" to do with 2 poles. <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

Alan

14. ## Re: How High?

I imagine the support structure for the second pole would be rather interesting. <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

15. ## Re: How High?

If one is a north pole and the other a south pole, they'd be rather cool...

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