A descending parachutist is acted on by two forces: a constant downward force mg and the...
A descending parachutist is acted on by two forces: a constant downward force mg and the upward force of air resistance, which (within close approximation) is of the form −βv2 where β is a positive constant. (In this problem we are taking the downward direction as positive.)
(a) Express t in terms of the velocity v, the initial velocity v0, and the constant vc =√mg/β.
(b) Express v as a function of t.
(c) Express the acceleration a, as a function of t. Verify that the acceleration never changes sign and in time tends to zero.
(d) Show that in time v tends to vc.(This number vc is called the terminal velocity.)
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A descending parachutist is acted on by two forces: a constant
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(Newton's 2nd law) Suppose a falling object of mass m is acted on by two forces: gravity, which acts down with magnitude mg, and a resistive force which acts up with magnitude 2v, where v is the velocity of the object. Does the object approach a terminal velocity? If so, find it.
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