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Consider an object with mass m dropped from rest. Assume that air resistance is proportional to...

Consider an object with mass m dropped from rest. Assume that air resistance is proportional to the square of the velocity of the object, with positive proportionality constant k. Let v(t) be the velocity after t seconds, and let g be the acceleration of the object due to gravity. The corresponding initial value problem is

mdv =mg−kv2; v(0)=0. dt

(a) Solve the initial value problem. Your answer will be in terms of m, k, and g.

(b) Compute lim v(t). What does this mean in the context of the problem? t→∞

(c) What happens to terminal velocity if m increases?

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