A model for the velocity of a falling object after time t is 

where m is the mass of the object, g = 9.8 m/s² is the acceleration due to gravity, k is a constant, t is measured in seconds, and v in mys.
(a) Calculate the terminal velocity of the object, that is, lim_{t→ ∞}(t).
(b) If a person falls from a building, the value of the constant k depends on his or her position. For a “belly-to-earth” position, k = 0.515 kg/s, but for a “feet-first” position, k = 0.067 kg/s. If a 60-kg person falls in belly-to-earth position, what is the terminal velocity? What about feetfirst?

|gk mg tanh v(t) = k