Consider again the baseball problem in Example 5. This time assume a drag coefficient of 0.08 and an instantaneous gust of wind that adds a component of -17.6i (ft/sec) to the initial velocity at the instant the baseball is hit.

a. Find a vector equation for the path of the baseball.

b. How high does the baseball go, and when does it reach maximum height?

c. Find the range and flight time of the baseball.

d. When is the baseball 35 ft high? How far (ground distance) is the baseball from home plate at that height?

e. A 20-ft-high outfield fence is 380 ft from home plate in the direction of the flight of the baseball. Has the batter hit a home run? If “yes,” what change in the horizontal component of the ball’s initial velocity would have kept the ball in the park? If “no,” what change would have allowed it to be a home run?

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EXAMPLE 5 A baseball is hit when it is 3 ft above the ground. It leaves the bat with initial speed of 152 ft/sec, making an angle of 20° with the horizontal. At the instant the ball is hit, an instantaneous gust of wind blows in the horizontal direction directly opposite the direction the ball is taking toward the outfield, adding a component of -8.8i (ft/sec) to the ball's initial velocity (8.8 ft/sec = 6 mph).