Solved: Hitting Bottom A helicopter hovers 500 feet above a large open tank full of

Chapter 3, Problem 25

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Hitting Bottom A helicopter hovers 500 feet above a large open tank full of liquid (not water). A dense compact object weighing 160 pounds is dropped (released from rest) from the helicopter into the liquid. Assume that air resistance is proportional to instantaneous velocity v while the object is in the air and that viscous damping is proportional to v2 after the object has entered the liquid. For air take k , and for the liquid take k 0.1. Assume that the positive direction is downward. If the tank is 75 feet high, determine the time and the impact velocity when the object hits the bottom of the tank. [Hint: Think in terms of two distinct IVPs. If you use (13), be careful in removing the absolute value sign. You might compare the velocity when the object hits the liquidthe initial velocity for the second problemwith the terminal velocity vt of the object falling through the liquid.]