Evaluate the dominant behavior

Reference no: EM1317877

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)?

Reference no: EM1317877

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