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40. Hitting a baseball under a wind gust A baseball is hit when it is 2.5 ft above the ground. It leaves the bat with an initial velocity of 145 ft/sec at a launch angle of 23°. At the instant the ball is hit, an instantaneous gust of wind blows against the ball, adding a component of –14i (ft/sec) to the ball's initial velocity. A 15-ft- high fence lies 300 ft from home plate in the direction of the flight. a. Find a vector equation for the path of the baseball. b. How high does the baseball go, and when does it reach maxi- mum height? c. Find the range and flight time of the baseball, assuming that the ball is not caught. d. When is the baseball 20 ft high? How far (ground distance) is the baseball from home plate at that height? e. Has the batter hit a home run? Explain.

40. Hitting a baseball under a wind gust A baseball is hit when it is 2.5 ft above the ground. It leaves the bat with an initial velocity of 145 ft/sec at a launch angle of 23°. At the instant the ball is hit, an instantaneous gust of wind blows against the ball, adding a component of –14i (ft/sec) to the ball's initial velocity. A 15-ft- high fence lies 300 ft from home plate in the direction of the flight. a. Find a vector equation for the path of the baseball. b. How high does the baseball go, and when does it reach maxi- mum height? c. Find the range and flight time of the baseball, assuming that the ball is not caught. d. When is the baseball 20 ft high? How far (ground distance) is the baseball from home plate at that height? e. Has the batter hit a home run? Explain.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Analytic Trigonometry
Section2.1: Using Fundamental Identities
Problem 67E
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40. Hitting a baseball under a wind gust A baseball is hit when it is 2.5 ft above the ground. It leaves the bat with an initial velocity of 145 ft/sec at a launch angle of 23°. At the instant the ball is hit, an instantaneous gust of wind blows against the ball, adding a component of –14i (ft/sec) to the ball's initial velocity. A 15-ft- high fence lies 300 ft from home plate in the direction of the flight. a. Find a vector equation for the path of the baseball. b. How high does the baseball go, and when does it reach maxi- mum height? c. Find the range and flight time of the baseball, assuming that the ball is not caught. d. When is the baseball 20 ft high? How far (ground distance) is the baseball from home plate at that height? e. Has the batter hit a home run? Explain.
Transcribed Image Text:40. Hitting a baseball under a wind gust A baseball is hit when it is 2.5 ft above the ground. It leaves the bat with an initial velocity of 145 ft/sec at a launch angle of 23°. At the instant the ball is hit, an instantaneous gust of wind blows against the ball, adding a component of –14i (ft/sec) to the ball's initial velocity. A 15-ft- high fence lies 300 ft from home plate in the direction of the flight. a. Find a vector equation for the path of the baseball. b. How high does the baseball go, and when does it reach maxi- mum height? c. Find the range and flight time of the baseball, assuming that the ball is not caught. d. When is the baseball 20 ft high? How far (ground distance) is the baseball from home plate at that height? e. Has the batter hit a home run? Explain.
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