Consider the 16-pound cannonball shot vertically upward in Problems 36 and 37 in Exercises 3.1 with an initial velocity v₀= 300 ft/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.

Data form problem 36 & 37 (Exercise 3.1)

Suppose a small cannonball weighing 16 pounds is shot vertically upward, as shown in the following figure, with an initial velocity v₀ = 300 ft/s. The answer to the question €œHow high does the cannonball go?€ depends on whether we take air resistance into account.

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mg ground level