Re:Longest Lines of Sight on Earth
by jnbiche on Thursday July 27, 2017 @08:23AM
(#14864578)
To be clear, they gave you the radius of the earth here, if you didn't already know it by heart? Otherwise, I'm not getting how you could solve this problem (assuming they didn't give you the angle that the arch formed, for example).
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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.
Re:Longest Lines of Sight on Earth
by jamesmaniscalco on Thursday July 27, 2017 @01:38PM
(#14867581)
I think this is the wrong interpretation; your answer would be correct if the rope were hovering at a height of 10 km along the full length.
My interpretation is that the rope is pulled taut to a height of 10 km at a single point, so that it runs in a straight line to the horizon in either direction and lays on the ground the rest of the way; this is also relevant to the question of longest line of sight from a given height.
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.