Chapter 1.1, Problem 9P

For small, slowly falling objects, the assumption made inEq. (i) of Problem 8 that the drag force is proportional to the velocity is a good one. For larger, more rapidly falling

objects, it is more accurate to assume that the drag force isproportional to the square of the velocity.

Write a differential equation for the velocity of a falling object of mass $m$ if the drag force is proportional to the square of the velocity. Assume that the upward direction is positive.

Determine the limiting velocity after a long time.

If $m=0.025$ kilograms (kg), find the drag coefficient so that the limiting velocity is $-35\text{m/s}$.