Physics, 12.03.2020 07:05, synite

A differential equation for the velocity of a falling mass m subjected to air resistance proportional to the square of the instantaneous velocity is m = m − 2 where > 0 is a constant of proportionality. The positive direction is downward. (a) Solve the equation subject to the initial condition (0) = 0. Hint: ∫ 2−2 = 1 tanh−1 ( ) + c (b)Use the solution in part (a) to determine the limiting, or terminal, velocity of the mass. That is, what happens to () as → [infinity]?

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A differential equation for the velocity of a falling mass m subjected to air resistance proportiona...