FYKOS Year 31 Series 6 Problem 5 — jump from a plane · FYKOS 31 #31.6.5

Physics · mechanics

Problem

Filip of mass 80 kg80 \mathrm{kg} jumped out of air plane, that is h1=500 mh_1 =500 \mathrm{m} above the ground. At the same time, Danka (mass 50 kg50 \mathrm{kg}) jumps out of a different airplane but from a height of h2=569 mh_2 =569 \mathrm{m}. Assume both of them have the same drag coefficient C=1,2C = 1{,}2, Filip's cross-sectional area is S_F=2,2 m2S\_F = 2{,}2 \mathrm{m^2} and Danka's is S_D=1,5 m2S\_D=1{,}5 \mathrm{m^2}. The density of air ρ=1,205 kg⋅m−3\rho =1{,}205 \mathrm{kg\cdot m^{-3}} is and stays the same in all heights. At what time will Danka be at the same height above the ground as Filip?

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