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Solved: PROBLEM 16EHow High—Nonlinear Air Resistance
Chapter 3, Problem 16E(choose chapter or problem)
How High?—Nonlinear Air Resistance Consider the 16-pound cannonball shot vertically upward in Problems 36 and 37 in Exercises 3.1 with an initial velocity \(v_{0}=300 \mathrm{ft} / \mathrm{s}\). Determine the maximum height attained by the cannonball if air resistance is assumed to be proportional to the square of the instantaneous velocity. Assume that the positive direction is upward and take k = 0.0003. [Hint: Slightly modify the DE in Problem 15.]
Text Transcription:
v_0 = 300 ft/s
Questions & Answers
QUESTION:
How High?—Nonlinear Air Resistance Consider the 16-pound cannonball shot vertically upward in Problems 36 and 37 in Exercises 3.1 with an initial velocity \(v_{0}=300 \mathrm{ft} / \mathrm{s}\). Determine the maximum height attained by the cannonball if air resistance is assumed to be proportional to the square of the instantaneous velocity. Assume that the positive direction is upward and take k = 0.0003. [Hint: Slightly modify the DE in Problem 15.]
Text Transcription:
v_0 = 300 ft/s
ANSWER:Step 1 of 5
In this problem we have to determine the maximum height attained by the 16 pound cannon ball
Which is shot vertically upwards considering the air resistance is proportional to square of the instantaneous velocity.
We have