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**Unformatted text preview: **, t D mg v = in agreement with Eq. (5.13). d) The equation of motion may be rewritten as ). ( 2 2 2 t v v t v g dt dv-= This is a separable equation and may be expressed as , arctanh 1 or , t 2 t t 2 t 2 2 t v gt v v v dt v g v v dv = =- so ( 29 . tanh t t v gt v v = Note : If inverse hyperbolic functions are unknown or undesirable, the integral can be done by partial fractions, in that , 1 1 2 1 1 t t t 2 2 t + +-=-v v v v v v v and the resulting logarithms in the integrals can be solved for ) ( t v in terms of exponentials....

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