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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.
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Results for Problem 3, high school students.
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