In our models of air resistance the resistance force has depended only on the velocity. However, for an object that drops a considerable distance, such as the parachutist in the previous exercise, there is a dependence on the altitude as well. It is reasonable to assume that the resistance force is proportional to air pressure, as well as to the velocity. Furthermore, to a first approximation the air pressure varies exponentially with the altitude (i.e., it is proportional to e–ax, where a is a constant and x is the altitude). Present a model using Newton’s second law for the motion of an object in the earth’s atmosphere subject to such a resistance force.
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