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Zagrepčanka Mystery Cache

Hidden : 5/5/2015
Difficulty:
3 out of 5
Terrain:
1.5 out of 5

Size: Size:   micro (micro)

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Geocache Description:


EN: You’re probably at home, looking at this mystery from your armchair. Or sitting on the chair at your work place (especially if you work for the government, then you’ll have a lot of free time). In any case, you think you are relatively static.

Wrong!

The Earth is spinning, together with everything and everyone on it. Which means that you, me, and everybody else on this tiny planet is travelling VERY fast. How fast?
Well, if you were standing exactly on North or South Pole, your speed would effectively be zero, the only movement would be a complete rotation around your axis every 24 hours.
So, this means that the fastest movement on the Earth would be on its equator. Circumference of the Earth at the Equator is around 40000 km, which you travel during the 24 hours, thus making your speed an astonishing 1666.67 km/h. Wow!!!

What is the speed of every citizen of Zagreb? Let's assume you're standing in front of Zagrepčanka building (the highest building in Croatia), on the given coordinates. Your speed woud be ABCD.EF km/h. (hint: it will be greater than 0, but less than 1666.67 ).

(ignore the speed of the Earth traveling around the sun, calculate only the rotation around the NE axis, and consider Earth to be a perfect sphere, with the circumference of 40000 km)

But, what would your speed be if you climb on top of Zagrepčanka building, you are probably wondering. If you’re not, you better start, because this is exactly what we’re looking for. Let’s say you climbed to the top of the antenna on the roof, which would place you 110 m above the street level. There, you will notice that your speed increased for GH *meters* per hour comparing it to the ground level speed. Round both numbers (F and H) to the closest decimal, and remember that Zagrepčanka tower is not in Pisa, but in Zagreb (thanks Siram!).

HR: Vjerojatno ste kod kuće, i gledate ovu misteriju iz svoje fotelje. Ili možda sjedite na stolici na poslu (pogotovo ako radite u državnoj službi, onda imate puno slobodnog vremena). U svakom slučaju, mislite da ste relativno statični.

Krivo!

Zemlja se okreće, a s njom i sve na njezinoj površini. To bi značilo da se vi, ja, i sva bića na Zemlji gibaju VELIKOM brzinom. Kolikom brzinom?
Pa, ako stojite direktno na Sjevernom ili Južnom Polu, vaša efektivna brzina će biti nula, jedino kretanje će vam biti kompletna rotacija oko vlastite osi svaka 24 sata.
Iz ovoga slijedi da je najveća brzina Zemlje na ekvatoru. Opseg Zemlje oko ekvatora je 40000 km, koje proputujete u 24 sata, pa time vaša brzina ispada nevjerovatnih 1666.67 km/h. Wow!!!

Koja je onda brzina svakog građanina Zagreba? Pretpostavimo da stojite pred Zagrepčankom (najviša zgrada u Hrvatskoj), na danim koordinatama. Brzina će vam u tom slučaju biti ABCD.EF km/h. (hint: bit će veća od 0, a manja od 1666.67 ).

(zanemarite brzinu Zemlje na putu oko Sunca, računate samo rotaciju oko zemljine osi, a Zemlju tretirajte kao savršenu kuglu opsega 40000 km)

Sigurno se pitate kolika bi vam bila brzina ako se popnete na vrh Zagrepčanke, je li tako? Ako ne, bolje se počnite pitati, jer se upravo to traži u zadatku.
Recimo da ste se popeli na vrh antene na krovu, koji je na 110 m iznad razine ulice. Tamo ćete primijetiti da se vaša brzina povećala za GH *metara* po satu u odnosu na brzinu na razini ulice. Zaokružimo oba broja (F i H) na najbližu decimalu, i prisjetimo se da Zagrepčanka nije u Pisi nego u Zagrebu (hvala Siram!).

Cache je at/Cache je na N 45° 47.NNN E 15° 57.EEE
NNN = (13*ABC-4*DEF+8*GH-4), EEE = (7*DEF-7*ABC+10*GH-1)

Additional Hints (Decrypt)

Urer, lbhe eryngvir fcrrq vf rira fznyyre guna ba gur tebhaq yriry. Biqwr wr inšn eryngvian oemvan wbš v znawn artb an enmvav hyvpr.

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)