Mathematical and Physical Journal
for High Schools
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# Problem P. 4728. (April 2015)

P. 4728. Philae, the lander of the space probe called Rosetta, landed on the nucleus of a comet of mass $\displaystyle 10^{13}$ kg, and of average density 0.4 g/cm$\displaystyle {}^3$, which is due to the fact that inside the nucleus there are voids. The landing was bouncy'', Philae arrived back to the surface of the nucleus of the comet 113 minutes later after its first bounce. Give estimation for the following:

$\displaystyle a)$ What is the gravitational field strength on the surface of the nucleus of the comet, and what is the escape speed?

$\displaystyle b)$ What was the least speed of the first bounce, and to what greatest height could Philae bounce back?

For the estimation, the nucleus of the comet can be considered as a uniform sphere, which is not rotating, and the motion can be considered as uniformly accelerated. For determining the average acceleration use the exact relationship between the speed and the height of the bouncing.

(5 pont)

Deadline expired on May 11, 2015.

### Statistics:

 47 students sent a solution. 5 points: Asztalos Bogdán, Balogh Menyhért, Bekes Nándor, Büki Máté, Csathó Botond, Csorba Benjámin, Fekete Balázs Attila, Fekete Panna, Forrai Botond, Holczer András, Iván Balázs, Jakus Balázs István, Kasza Bence, Kormányos Hanna Rebeka, Körtefái Dóra, Marozsák Tóbiás , Németh Flóra Boróka, Olosz Balázs, Páhoki Tamás, Sal Kristóf, Szentivánszki Soma , Zöllner András. 4 points: Berta Dénes, Blum Balázs, Boldizsár Bálint, Bugár 123 Dávid, Csire Roland, Csurgai-Horváth Bálint, Fehér Balázs, Fülöp Erik, Horváth Botond István, Kovács Péter Tamás, Mándoki László, Öreg Botond, Pázmán Előd, Pszota Máté, Sallai Krisztina, Simon Dániel Gábor, Valus Dávid, Varga-Umbrich Eszter, Vastag Balázs. 3 points: 2 students. 2 points: 4 students.

Problems in Physics of KöMaL, April 2015