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For a ball of mass m > 0 with velocity v in the direction of the...

For a ball of mass m > 0 with velocity v in the direction of the earth, the velocity obeys the differential equation

v˙ = g − (κ/m)v2

where g > 0 is the gravitational constant and κ > 0 is a constant of air resistence.

(a) Classify all critical points.

(b) Explain the long term behavior for every initial condition. When is this model for air resistence physically realistic?

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