FYKOS Year 26 Series 2 Problem 1 — from Prague to Brno · FYKOS 26 #26.2.1

Physics · mechanics

Problem

Assume that the Earth is a sphere and the surface distance between Dresden and Vienna is approximately d=370d=370 km. How much is the distance reduced if you decide to dig a tunnel between those two cities instead of walking. Neglect the different altitudes. Compare the tunnel distance with walking distance. For simplicity, you can approximate trigonometric functions as sinα≈α−α3/6 ,cosα≈1−α2/2 ,tgα≈α+α3/3 ,\mathrm{sin} α ≈ α - α^{3}/6 \,, \mathrm{cos} α ≈ 1 - α^{2}/2 \,, \mathrm{tg} α ≈ α + α^{3}/3 \,, where the angle is assumed to be given in radians.

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