Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §6.7 Hyperbolic Functions, #54 · Calculus · Differentiation rules

A falling body with friction equal to velocity squared obeys

A falling body with friction equal to velocity squared obeys $d v / d t = g - v^{2}$ .
(a) Show that $v (t) = g tanh g t$ satisfies the equation.
(b) Derive this $v$ yourself, by integrating $d v / (g - v^{2}) = d t$ .
(c) Integrate $v (t)$ to find the distance $f (t)$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §6.7 Hyperbolic Functions, #54

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