An object masses 10 kg, has a frontal area of 0.3 m2, and a drag coefficient

of 1.1. This object is dropped from an airplane flying at 5000 m (initial vertical velocity is zero). The horizontal velocity plays no role—it can also be taken as zero. The atmospheric density (in kg/m3) is a function of height and is given by ρ = 1.29 exp − h 8000. The height, h, is in meters above sea level. Assume that the acceleration of gravity, g, is height independent. Describe quantitatively what happens. Calculate the maximum vertical velocity acquired by the object. This will lead to a differential equation. Do not attempt to solve it analytically. Use a numerical solution with a time step of 1 second. Few iterations will be needed, and notwithstanding the very coarse time steps, will yield a good estimate of the velocity. Surprisingly, you will overestimate the correct velocity by less than 0.5%.

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