Mathematical and Physical Journal
for High Schools
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# Problem P. 4248. (April 2010)

P. 4248. In calm weather a rope, which is attached to a spherical balloon filled with Helium, hangs vertically and tight. In wind, however, in one case the rope makes an angle of 20o with the vertical, and in a second case an angle of 55o. Determine the ratio of the wind speeds in the two cases, provided that the air drag is proportional to the square of the speed of the wind.

(4 pont)

Deadline expired on May 10, 2010.

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

Megoldás. $\displaystyle v_2/v_1=\sqrt{ \tg\varphi_1/ \tg\varphi_2}\approx2,\!0$. (Feltételeztük, hogy a felhajtóerő áramló levegő esetén is ugyanakkora, mint a sztatikus esetben. Ez szigorúan véve nem igaz, de az eltérés figyelembe vétele nyilván meghaladja a középiskolai ismereteket.)

### Statistics:

 88 students sent a solution. 4 points: 55 students. 3 points: 11 students. 2 points: 10 students. 1 point: 3 students. 0 point: 9 students.

Problems in Physics of KöMaL, April 2010