# Physics Cup – TalTech 2019, 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 FosterJohanes 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

 name country school solved score Siddharth Tiwary India Indian Inst. of Techn. Bombay 10 Feb. 2019 14:38 2.594 Thomas Foster UK University of Oxford 10 Feb. 2019 16:16 3.291 Johanes Suhardjo Indonesia Hong Kong Univ Sci & Tech 10 Feb. 2019 17:15 2.992 Damiano Tietto Italy Università degli Studi di Padova 10 Feb. 2019 17:49 1.754 Ivan Ridkokasha Ukraine Shevchenko University Kyiv 10 Feb. 2019 18:57 1.772 Marcell Szakály Hungary University of Cambridge 11 Feb. 2019 00:13 1.611 Aaditya Mishra India Indian Institute of Sci. Ed. and Research 16 Feb. 2019 07:16 1.464 Roshan Kaundinya India Indian Institute of Sci. Ed. and Research 17 Feb. 2019 09:23 1.331 Petra Brčić Croatia University of Zagreb 17 Feb. 2019 10:50 1.21 Yasin Sönmez & Batuhan Keskin Turkey Boğaziçi University 17 Feb. 2019 18:01 1.045 Felix Bekir Christensen Germany University of Oxford 02 Mar. 2019 11:17 1 Eugen Dizer Germany University of Heidelberg 07 Mar. 2019 01:03 1 Philipp Schange Germany WWU Münster 07 Mar. 2019 12:21 1

Results for Problem 3, high school students

 name country school solved score Ionel-Emilian Chiosa Romania Intern Computer HS Bucharest 10 Feb. 2019 15:55 3.258 Marvin Janini Brazil Colégio Etapa 10 Feb. 2019 16:55 2.24 Tùng Trần Xuân Vietnam HN-Amsterdam 10 Feb. 2019 17:26 2.144 Domagoj Perković Croatia III. Gigmazija Split 10 Feb. 2019 18:30 1.949 Eduard Burlacu Romania Intern Computer HS Bucharest 10 Feb. 2019 19:44 1.772 Stefan Dolteanu Romania Intern Computer HS Bucharest 10 Feb. 2019 16:14 1.611 Gabriel Trigo Brazil Colegio ETAPA, Valinhos 11 Feb. 2019 02:37 1.464 Roberto Marín Delgado Costa Rica Colegio Científico San Carlos 11 Feb. 2019 05:17 1.464 Oliver Lindström Sweden Minervagymnasium 11 Feb. 2019 10:25 1.21 Vladislav Polyakov Russia School No 23 St Petersburg 11 Feb. 2019 11:16 1.1 Ivander J.M. Waskito Indonesia Mawar Sharon Christian School 11 Feb. 2019 16:12 1 Zăhărăchescu Mihai Romania Intern Computer HS Bucharest 11 Jan. 2019 17:06 1 Masuk Ridwan Bangladesh St. Joseph Higher Secondary S. 12 Feb. 2019 11:51 1 Oliwier Urbański Poland Szkoła Nr 28 w Poznaniu 12 Feb. 2019 20:51 1 Domonkos Svastits Hungary Piarist High School 12 Feb. 2019 21:05 1 Bakir Devedžić Bosnia and Herz. Gymnasium “Dr. Mustafa Kamarić” 13 Feb. 2019 03:18 0.95 Siam Absur Khan Bangladesh Ideal School And College 13 Feb. 2019 11:22 1 Timothy Ho Singapore NUS High School of Math. and Sci. 16 Feb. 2019 09:32 1 Erik Swanson New York Queensbury High School 16 Feb. 2019 10:46 1 Eduardo Bardal Slikta Brazil Colégio Etapa Valinhos 17 Feb. 2019 06:06 1 Domantas Burba Lithuania Siauliai Julius Janonis Gymnasium 17 Feb. 2019 11:41 1 Vaibhav Raj India Allen Kota School 17 Feb. 2019 13:56 1 Vinícius Ferreira Rodrigues Brazil Colégio Master 20 Feb. 2019 12:20 1 Mateusz Kapusta Poland Secondary School No. III, Wroclaw 21 Feb. 2019 20:03 1 Stephen Catsamas Australia Marcellin College 23 Feb. 2019 17:43 1 Morteza Mudrick Indonesia SMA Negeri 1 Surakarta 24 Feb. 2019 12:56 0.9 Bartłomiej Sikorski Poland I Liceum O. Starachowicach 24 Feb. 2019 18:13 1 Jaeyong Lee Korea Dongsan High School 24 Feb. 2019 19:24 1 Dhyaan S. Nayak India National Institute of Open Schooling 25 Feb. 2019 09:06 0.95 Richard Luhtaru Estonia Hugo Treffner Gymnasium 26 Feb. 2019 17:19 1 Ayush Anand India Neel Kamal Sethia 28 Feb. 2019 05:57 1 Kaviraj Prithvi India Base PU College 01 Mar. 2019 13:59 0.9 Jianzhi Wang Singapore Raffles Institution 02 Mar. 2019 04:02 1 Muhamed Sokolović Bosnia and Herz. Richmond Park ISS Sarajevo 02 Mar. 2019 10:11 1 Esha Manideep Dinne India Pre-University 02 Mar. 2019 12:19 1 Tádé Marozsák Hungary Óbudai Árpád Gimnázium 02 Mar. 2019 18:42 1 Łukasz Basiński Poland II Liceum Ogólnokształcące im. Jana Śniadeckiego w Kielcach 04 Mar. 2019 19:32 0.95 Thanawat Sornwanee Thailand Triamudomsuksa School 05 Mar. 2019 01:01 1 Yogit Shankar India Hope hall foundation School 05 Mar. 2019 07:55 1 Lucas Harada Brazil Colegio Etapa – Ana Rosa 07 Mar. 2019 02:52 1 Pradipta Parag Bora India Delhi Public School Guwahati 07 Mar. 2019 07:23 1 Ananjan Nandi India Resonance Kota 07 Mar. 2019 15:12 1 Gusti P.S.G. Atmaja Indonesia Kesatuan Bangsa SHS 10 Mar. 2019 11:33 1 Jānis Hūns Latvia Riga State Gymnasium No.1 10 Mar. 2019 13:02 1