Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Longest Lines of Sight on Earth

beyondhorizons.eu

Post reply on HN
Print view View original

151–160 of 164 posts

Re: Longest Lines of Sight on Earth

#151

Post by SamReidHughes »

seanmcdirmid wrote: post #52
kovek wrote: post #42

Earlier quoted context omitted.

I had this question worded differently asked to me when I interviewed to do an undergrad at Cambridge. If you have a rope that is wrapped around earth and you lift it off the ground as much as possible, and you see that it is 10km above the ground, then how long is the rope? I was not able to answer that question right away, and their hint to draw it helped a lot. I did not end up getting accepted.

It seems like one of those stupid brain teasers tech companies used to ask that are not very correlated with success but act as arbitrary filters.

That's a very straightforward math problem.

Re: Longest Lines of Sight on Earth

#152

Post by ivanbakel »

jnbiche wrote: post #150
ivanbakel wrote: post #135

Earlier quoted context omitted.

You don't need to know the radius of the earth unless you're asked for a numeric answer. The rope is 2 * pi * 10km longer than the Earth's circumference, since its radius is 10km more.

Actually, it's a different question. Check out the second diagram linked to below: https://news.ycombinator.com/item?id=14863949 So yes, you could supply the answer in terms of r radius, but you do need to know the radius unless I'm missing something obvious.

That diagram wasn't posted by the GP.

Re: Longest Lines of Sight on Earth

#153

Post by jwilk »

liuhenry wrote: post #85
kijin wrote: post #78

Earlier quoted context omitted.

That question is ambiguous. If you only need a single cat to go under the rope at some point, you just add a small arch for the cat to walk through. This requires a length of rope somewhat less than twice the height of the cat. 2 x Pi x Cat would levitate the rope by the height of the cat along the entire circumference of the Earth, allowing a billion cats to go under it simultaneously. You could even make do with no…

The answer to the first interpretation is considerably less than twice the height of the cat, and I think it's an interesting result as well: Assuming a 0.3 meter high cat, you only need ~0.12mm of extra rope (about the width of two sheets of paper) to be able to pull it up at a point and let the cat through.

Here's the calculation:

https://upload.wikimedia.org/wikipedia/commons/2/21/Geometri...

R ≈ 6.4E6

h = 0.3

d = √(2Rh + h²) ≈ 2.0E3

γ ≈ sin γ = d/(R + h) ≈ 3.1E-4

extra rope length = 2 × (d − γR) = 2R × (tan γ − γ) ≈ 2R × γ³/3 ≈ 0.13E-3

Re: Longest Lines of Sight on Earth

#154

Post by Dove »

seanmcdirmid wrote: post #52
kovek wrote: post #42

Earlier quoted context omitted.

I had this question worded differently asked to me when I interviewed to do an undergrad at Cambridge. If you have a rope that is wrapped around earth and you lift it off the ground as much as possible, and you see that it is 10km above the ground, then how long is the rope? I was not able to answer that question right away, and their hint to draw it helped a lot. I did not end up getting accepted.

It seems like one of those stupid brain teasers tech companies used to ask that are not very correlated with success but act as arbitrary filters.

I don't see anything tricky about that problem. It requires some junior high geometry and high school trig, and yes, I suppose you need to know the radius of the earth offhand. Still. That strikes me a lot more as a math fizzbuzz than as a brain teaser. A college applicant can be reasonably expected to know this stuff.

Re: Longest Lines of Sight on Earth

#155

Post by Nition »

btilly wrote: post #149
gmiller123456 wrote: post #147

Earlier quoted context omitted.

This is too simplistic of an approach. Suppose there is another 6km tall mountain just beyond the horizon, it will have a farther line of site to the peak of it than to the horizon just in front of it. This list seems to be a much more rigorous attempt.

Too simplistic of an approach for what? It is meant to show how to calculate the position of the horizon on a smooth planet. Obviously your line of sight typically includes tall things beyond the horizon. However this calculation lets you know both how far away your horizon is, and how far beyond that a tall object could be seen if nothing else was in the way. Which puts an upper limit on how far away it can be. A li…

I think gmiller123456 just missed the fact that you did account for a second mountain over the horizon. Your post was great, thanks for writing it up.

Re: Longest Lines of Sight on Earth

#156

Post by YZF »

Nition wrote: post #99
YZF wrote: post #57

Earlier quoted context omitted.

The version I got, in a tech company interview, was how much longer would you need to make the rope to allow a cat to go under it. They were basically just look for 2 x Pi x Cat in this case.

I think that's a bit different. I tried to draw a diagram: http://i.imgur.com/XT3uGdM.png If kovek's question was like the first image there, it'd be a simple radius/circumference calculation (2 * pi * 5km). But it sounds like the second image to me - which makes it into more of a horizon line problem.

Yeah, I know that. I'm just trying to add to the history of rope/earth/cat interview questions here. This was ~15 years ago by the way and to be clear we're talking about cats being able to pass anywhere, not the line of sight problem, which I agree makes it a little more interesting..,

Re: Longest Lines of Sight on Earth

#157

Post by seanmcdirmid »

SamReidHughes wrote: post #151
seanmcdirmid wrote: post #52

Earlier quoted context omitted.

It seems like one of those stupid brain teasers tech companies used to ask that are not very correlated with success but act as arbitrary filters.

That's a very straightforward math problem.

There is a lot more than the Pythagorean theorem in that question. It would require remember a lot of middle school theorems from a long time ago; frankly calculus would be better.

Re: Longest Lines of Sight on Earth

#159

Post by jnbiche »

ivanbakel wrote: post #152
jnbiche wrote: post #150

Earlier quoted context omitted.

Actually, it's a different question. Check out the second diagram linked to below: https://news.ycombinator.com/item?id=14863949 So yes, you could supply the answer in terms of r radius, but you do need to know the radius unless I'm missing something obvious.

That diagram wasn't posted by the GP.

Yes, but I only posted that so you'd see which problem the GP is referring to: the second one. Unless somehow the rope is some special kind of non-flexible rope that always assumes the shape of a circle.

Re: Longest Lines of Sight on Earth

#160

Post by ivanbakel »

jnbiche wrote: post #159
ivanbakel wrote: post #152

Earlier quoted context omitted.

That diagram wasn't posted by the GP.

Yes, but I only posted that so you'd see which problem the GP is referring to: the second one. Unless somehow the rope is some special kind of non-flexible rope that always assumes the shape of a circle.

What makes you think that's the problem the GP was referring to? They haven't posted at all again in this thread to confirm exactly what was meant.
Post reply on HN