Problems 16 through 18 deal with the batted baseball of Example 4, having initial velocity 160 ft/s and air resistance coefficient c = 0.0025.

Find the range—the horizontal distance the ball travels before it hits the ground—and its total time of flight with initial inclination angles 40°, 45°, and 50°.

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Example 4 Batted baseball Suppose that a batted ball starts at x = 0, yo=0 with initial velocity Vo = 160 ft/s and with initial angle of inclination 0 = 30°. If air resistance is ignored, we find by the elementary methods of Section 1.2 that the baseball travels a [horizontal] distance of 400 √3 ft (approximately 693 ft) in 5 s before striking the ground. Now suppose that in addition to a downward gravitational acceleration (g = 32 ft/s²), the baseball experiences an acceleration due to air resistance of (0.0025) v² feet per second per second, directed op- posite to its instantaneous direction of motion. Determine how far the baseball will travel horizontally under these conditions.