Mathematical and Physical Journal
for High Schools
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Problem P. 4436. (April 2012)

P. 4436. A tour boat departed at Siófok travelled at a constant speed of 18 km/h, first moved towards the North for a quarter of an hour, then it turned and travelled another quarter of an hour towards the West, then again turned and travelled a quarter of an hour towards the South, and then finally it travelled towards the East for a quarter of an hour.

a) Consider the curvature of the Earth and estimate how far will the tour boat be from the starting point at the end of the tour.

b) The mass of the boat is 500 tons. By what amount was the weight of the boat smaller when the boat travelled towards the East than when it travelled towards the West?

(4 pont)

Deadline expired on May 10, 2012.


Sorry, the solution is available only in Hungarian. Google translation

Megoldásvázlat. a) Égtájanként s=vt út megtétele után a kezdő- és a végpont távolsága

\frac{s^2}{R} \mathop{\rm tg}\nolimits 47^\circ\approx 3,4~ \rm m.

b) A súlykülönbség

4mv\omegacos 47o\approx50 N.


Statistics:

60 students sent a solution.
4 points:Demeter Dániel, Fehér Zsombor, Papp Roland, Vajda Balázs.
3 points:Beke Gabriella, Bolgár Dániel, Buttinger Milán, Csáky Pál, Csathó Botond, Csipor János, Czigány Máté Gábor, Fülep Andrea , Havasi 0 Márton, Hegyfalvi Csaba, Holczer András, Horicsányi Attila, Horváth András Levente, Juhász Péter, Kaposvári Péter, Kollarics Sándor, Laczkó Zoltán Balázs, Sárvári Péter, Szigeti Bertalan György.
2 points:16 students.
1 point:12 students.
0 point:9 students.

Problems in Physics of KöMaL, April 2012