Problem P. 4290. (November 2010)

P. 4290. A thin, strong steel cable is stretched horizontally, with a great force, above a street. A rope dancer walks along the cable. When she covers one-fourth of the length of the cable, (she is at point N) the trisecting point of the cable (H) is 10 cm below its original position. What will the decent of the point N be, when the rope dancer is at point H? (The mass of the cable is negligible, the deflection of the rope is very small with respect to the length of the cable, and the tension in the cable can be considered constant.)

(5 pont)

Deadline expired on December 10, 2010.

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

Megoldás. Az \(\displaystyle N\) pont lesüllyedése is éppen 10 cm lesz. (Ez az érdekes szimmetriatulajdonság a kötél tetszőleges két pontjára igaz.)

Statistics:

31 students sent a solution.
5 points:	Batki Bálint, Béres Bertold, Bolgár Dániel, Dinev Georgi, Gargauly Gergő János, Juhász Péter, Laczkó Zoltán Balázs, Mázik László, Nagy Dániel Bálint, Pázmán Koppány, Szabó 928 Attila, Szélig Áron, Szikszai Lőrinc, Várnai Péter.
4 points:	Antalicz Balázs, Barta Szilveszter Marcell, Szigeti Bertalan György.
3 points:	1 student.
2 points:	2 students.
1 point:	9 students.
0 point:	2 students.

Problems in Physics of KöMaL, November 2010