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3. An object of mass m is dropped into the sea at the surface. It is subject to a constant gravitational acceleration g and water

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3. An object of mass m is dropped into the sea at the surface. It is subject to a constant gravitational acceleration g and water resistance. (a) (6 points) If the water resistance is preportional to the object's velocity v(t) with coef- cient b > 0, so that Newton's second law gives show that the object's velocity as a function of time t is given by v(t) = $(1- c'bt/m) We take dewnward to be the positive direction and the object is at rest when it is dropped at f. = 0. (b) (6 points) If instead the water resistance is quadratic in the velocity3 so that Newton's second lav;r gives nd the ob ject's velocity as a function of time t, again assuming that the object is dropped from rest. [Hintz Write Newtons' law as 21; = g (1 22112) where k = v/b/mg. Then the algebra is a little less messy. After obtaining the final answer in terms of k, remember to replace k by y/bg (c) (2 points) If the object could fall forever under these conditions without hitting the bot- tom= show that as t > co the velocity in part (a) approaches terminal velocity v > El}. What terminal velocity does the velocity in part (b) approach

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