Free fall One possible model that describes the free fall of an object in a gravitational field subject to air resistance uses the equation v′(t) = g – bv, where v(t) is the velocity of the object for t ≥ 0, g = 9.8 m/s2 is the acceleration due to gravity, and b > 0 is a constant that involves the mass of the object and the air resistance.
a. Verify by substitution that a solution of the equation, subject to the initial condition v(0) = 0, is
b. Graph the solution with b = 0.1 s–1.
c. Using the graph in part (c), estimate the terminal velocity
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