Physics Cup – TalTech 2019, Problem 3

Problem 3

Results and best solutions

The third problem turned out to be easier than expected. Many contestants were able to reach the final answer by carrying out tedious calculations involving coordinate geometry. This brute-force approach requires confident handling of long algebraic formulas which is an important skill in physics (and physics competitions in particular). However, there is a shorter tricky solution (also suggested by the hints) which leads to the answer in a few lines. This solution relies on the geometrical properties of conic sections, such as the relation between the directrix and the focus point, and the reflective property of the parabola.

In total, 75 solutions of problem 3 were submitted out of which 56 were correct.

The best solution awards go to: Thomas Foster, Johanes Suhardjo and Ionel-Emilian Chiosa. All of them get 33.3% of the bonus.

All three solutions contain the tricky approach in a slightly different way. Thomas Foster uses the angles at the end and proves that the shape is a straight line by induction. Johanes Suhardjo presents two different methods, the first is a shorter one with elementary geometry, the second one is more algebraic. Altough the paper submitted by Ionel-Emilian Chiosa is handwritten, his solution is easy to follow and very elegant.

The additionally published solution is submitted by Roberto Marín Delgado, who is awarded by a bonus of factor 1.1. He uses the coordinate geometrical approach, but the solution is short, well written and drawn.

Results for Problem 3, university students

namecountryschoolsolvedscore
Siddharth TiwaryIndiaIndian Inst. of Techn. Bombay10 Feb. 2019 14:382.594
Thomas FosterUKUniversity of Oxford10 Feb. 2019 16:163.291
Johanes SuhardjoIndonesiaHong Kong Univ Sci & Tech10 Feb. 2019 17:152.992
Damiano TiettoItalyUniversità degli Studi di Padova 10 Feb. 2019 17:491.754
Ivan RidkokashaUkraineShevchenko University Kyiv10 Feb. 2019 18:571.772
Marcell SzakályHungaryUniversity of Cambridge11 Feb. 2019 00:131.611
Aaditya MishraIndiaIndian Institute of Sci. Ed. and Research16 Feb. 2019 07:161.464
Roshan KaundinyaIndiaIndian Institute of Sci. Ed. and Research17 Feb. 2019 09:231.331
Petra BrčićCroatiaUniversity of Zagreb17 Feb. 2019 10:501.21
Yasin Sönmez & Batuhan KeskinTurkeyBoğaziçi University17 Feb. 2019 18:011.045
Felix Bekir ChristensenGermanyUniversity of Oxford02 Mar. 2019 11:171
Eugen DizerGermanyUniversity of Heidelberg07 Mar. 2019 01:031
Philipp SchangeGermanyWWU Münster07 Mar. 2019 12:211

Results for Problem 3, high school students

namecountryschoolsolvedscore
Ionel-Emilian ChiosaRomaniaIntern Computer HS Bucharest10 Feb. 2019 15:553.258
Marvin JaniniBrazilColégio Etapa10 Feb. 2019 16:552.24
Tùng Trần XuânVietnamHN-Amsterdam10 Feb. 2019 17:262.144
Domagoj PerkovićCroatiaIII. Gigmazija Split10 Feb. 2019 18:301.949
Eduard BurlacuRomaniaIntern Computer HS Bucharest10 Feb. 2019 19:441.772
Stefan DolteanuRomaniaIntern Computer HS Bucharest10 Feb. 2019 16:141.611
Gabriel TrigoBrazilColegio ETAPA, Valinhos11 Feb. 2019 02:371.464
Roberto Marín DelgadoCosta RicaColegio Científico San Carlos11 Feb. 2019 05:171.464
Oliver LindströmSwedenMinervagymnasium11 Feb. 2019 10:251.21
Vladislav PolyakovRussiaSchool No 23 St Petersburg11 Feb. 2019 11:161.1
Ivander J.M. WaskitoIndonesiaMawar Sharon Christian School11 Feb. 2019 16:121
Zăhărăchescu MihaiRomaniaIntern Computer HS Bucharest11 Jan. 2019 17:061
Masuk RidwanBangladeshSt. Joseph Higher Secondary S.12 Feb. 2019 11:511
Oliwier UrbańskiPolandSzkoła Nr 28 w Poznaniu12 Feb. 2019 20:511
Domonkos SvastitsHungaryPiarist High School12 Feb. 2019 21:051
Bakir DevedžićBosnia and Herz.Gymnasium “Dr. Mustafa Kamarić”13 Feb. 2019 03:180.95
Siam Absur KhanBangladeshIdeal School And College13 Feb. 2019 11:221
Timothy HoSingaporeNUS High School of Math. and Sci.16 Feb. 2019 09:321
Erik SwansonNew YorkQueensbury High School16 Feb. 2019 10:461
Eduardo Bardal SliktaBrazilColégio Etapa Valinhos17 Feb. 2019 06:061
Domantas BurbaLithuaniaSiauliai Julius Janonis Gymnasium17 Feb. 2019 11:411
Vaibhav RajIndiaAllen Kota School17 Feb. 2019 13:561
Vinícius Ferreira RodriguesBrazilColégio Master20 Feb. 2019 12:201
Mateusz KapustaPolandSecondary School No. III, Wroclaw21 Feb. 2019 20:031
Stephen CatsamasAustraliaMarcellin College23 Feb. 2019 17:431
Morteza MudrickIndonesiaSMA Negeri 1 Surakarta24 Feb. 2019 12:560.9
Bartłomiej SikorskiPolandI Liceum O. Starachowicach24 Feb. 2019 18:131
Jaeyong LeeKoreaDongsan High School24 Feb. 2019 19:241
Dhyaan S. NayakIndiaNational Institute of Open Schooling25 Feb. 2019 09:060.95
Richard LuhtaruEstoniaHugo Treffner Gymnasium26 Feb. 2019 17:191
Ayush AnandIndiaNeel Kamal Sethia28 Feb. 2019 05:571
Kaviraj PrithviIndiaBase PU College01 Mar. 2019 13:590.9
Jianzhi WangSingaporeRaffles Institution02 Mar. 2019 04:021
Muhamed SokolovićBosnia and Herz.Richmond Park ISS Sarajevo02 Mar. 2019 10:111
Esha Manideep DinneIndiaPre-University02 Mar. 2019 12:191
Tádé MarozsákHungaryÓbudai Árpád Gimnázium02 Mar. 2019 18:421
Łukasz BasińskiPolandII Liceum Ogólnokształcące im.
Jana Śniadeckiego w Kielcach		04 Mar. 2019 19:320.95
Thanawat SornwaneeThailandTriamudomsuksa School05 Mar. 2019 01:011
Yogit ShankarIndiaHope hall foundation School05 Mar. 2019 07:551
Lucas HaradaBrazilColegio Etapa – Ana Rosa07 Mar. 2019 02:521
Pradipta Parag BoraIndiaDelhi Public School Guwahati07 Mar. 2019 07:231
Ananjan NandiIndiaResonance Kota07 Mar. 2019 15:121
Gusti P.S.G. AtmajaIndonesiaKesatuan Bangsa SHS10 Mar. 2019 11:331
Jānis HūnsLatviaRiga State Gymnasium No.110 Mar. 2019 13:021