Problem P. 3806. (May 2005)
P. 3806. A soldier has to cross a 60 m wide river on a ropeway grabbing on a pulley. The length of the rope is 75 m, its ends are fixed at the same height on both banks of the river. The soldier, whose mass together with his combat gear is 90 kg, starts from a platform under one of the fixed points with zero initial velocity.
a) What is the highest velocity of the soldier during the crossing?
b) What is the force exerted on the rope at that moment? (Take the rope as inextensible, weightless and free of any friction.)
Deadline expired on June 13, 2005.
117 students sent a solution. 5 points: Almási 270 Gábor, Bana Péter, Buday Péter, Darázs Zoltán, Demeter Dániel, Domonkos Tamás, Dudás János, Enczel Dávid, Filep Tamás, Filep Tibor, Hidasi Balázs, K. Gergely, Keresztes Szabolcs, Kolcza Mátyás Barna, Kónya 495 Gábor, Lantos Judit, Meszéna Balázs, Mezei Bálint, Molnár 811 Kristóf, Nagy 317 Péter, Nagy 555 Zoltán, Nyíri Dávid Ákos, Pálinkás Csaba, Pálovics Róbert, Pásztor 001 Attila, Paulin Roland, Pósa László, Strenner Balázs, Szabó 679 Dániel, Széchenyi Gábor, Szilágyi Zsombor, Szolnoki Lénárd, Takátsy Balázs, Varga 316 Lilla, Werner Miklós. 4 points: Fülöp Bálint, Tóth 324 Gábor. 3 points: 13 students. 2 points: 58 students. 1 point: 4 students. 0 point: 5 students.