Taylor expansion to find the dominant behavior of velocity.
If an object with mass m falls from rest subject to a certain type of air resistance, then its velocity at time t is given by
V(t) = (mg/c) (e-ct/m - 1)
Where g,c are constants (g is the acceleration due to gravity and c is a constant coming from the air resistance).
(a)If we assume that ct is much smaller than m, use a Taylor expansion to determine the dominant behavior of v(t), and also the first correlation to that dominant behavior.
(b)If we assume that m = 1 kg, g = 10 m/s2, and e = 0.02 kg/s, by what time will the first correlation be 10% or greater in size than the size of the dominant term in the expansion of v(t)?