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The knuckleball is one of the most exotic pitches in baseball. Batters describe the ball as unpredictably moving left, right, up, and down. For a typical knuckleball speed of 60 mph, the left/right position of the ball (in feet) as it crosses the plate is given by 1.7 f(w) = sin(2.72w) 8w2 %3D (derived from experimental data in Watts and Bahill's book Keeping Your Eye on the BallI), where w is the rotational speed of the ball in radians per second and where f(@) = 0 corresponds to the middle of home plate. Folk wisdom among baseball pitchers has it that the less spin on the ball, the better the pitch. To investigate this theory, we consider the lim f(w). (1) Evaluate the lim f(@) using the graphical and tabular approaches. Use the first quadrant of the Cartesian plane in sketching the graph. (2) A knuckleball thrown with a different grip than that of the problem above has left/right position as it crosses the plate given by

The knuckleball is one of the most exotic pitches in baseball. Batters describe the ball as unpredictably moving left, right, up, and down. For a typical knuckleball speed of 60 mph, the left/right position of the ball (in feet) as it crosses the plate is given by 1.7 f(w) = sin(2.72w) 8w2 %3D (derived from experimental data in Watts and Bahill's book Keeping Your Eye on the BallI), where w is the rotational speed of the ball in radians per second and where f(@) = 0 corresponds to the middle of home plate. Folk wisdom among baseball pitchers has it that the less spin on the ball, the better the pitch. To investigate this theory, we consider the lim f(w). (1) Evaluate the lim f(@) using the graphical and tabular approaches. Use the first quadrant of the Cartesian plane in sketching the graph. (2) A knuckleball thrown with a different grip than that of the problem above has left/right position as it crosses the plate given by

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Analysis: Real-life Application The knuckleball is one of the most exotic pitches in baseball. Batters describe the ball as unpredictably moving left, right, up, and down. For a typical knuckleball speed of 60 mph, the left/right position of the ball (in feet) as it crosses the plate is given by 1.7 f(@) = sin(2.72w) 8w? (derived from experimental data in Watts and Bahill's book Keeping Your Eye on the BallI), where w is the rotational speed of the ball in radians per second and where f(@) = 0 corresponds to the middle of home plate. Folk wisdom among baseball pitchers has it that the less spin on the ball, the better the pitch. To investigate this theory, we consider the lim f(w). (1) Evaluate the lim f(@) using the graphical and tabular approaches. Use the first quadrant of the Cartesian plane in sketching the graph. (2) A knuckleball thrown with a different grip than that of the problem above has left/right position as it crosses the plate given by 0.625 f(w) = - [1 – sın (2.72w + )| – sin Again, use graphical and tabular evidence to make a conjecture about the lim f(w).
Transcribed Image Text:Analysis: Real-life Application The knuckleball is one of the most exotic pitches in baseball. Batters describe the ball as unpredictably moving left, right, up, and down. For a typical knuckleball speed of 60 mph, the left/right position of the ball (in feet) as it crosses the plate is given by 1.7 f(@) = sin(2.72w) 8w? (derived from experimental data in Watts and Bahill's book Keeping Your Eye on the BallI), where w is the rotational speed of the ball in radians per second and where f(@) = 0 corresponds to the middle of home plate. Folk wisdom among baseball pitchers has it that the less spin on the ball, the better the pitch. To investigate this theory, we consider the lim f(w). (1) Evaluate the lim f(@) using the graphical and tabular approaches. Use the first quadrant of the Cartesian plane in sketching the graph. (2) A knuckleball thrown with a different grip than that of the problem above has left/right position as it crosses the plate given by 0.625 f(w) = - [1 – sın (2.72w + )| – sin Again, use graphical and tabular evidence to make a conjecture about the lim f(w).
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