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(b) At what time(s) is the height of the ball 52 feet? (Enter your answers as a comma-separated list.) t = sec

(b) At what time(s) is the height of the ball 52 feet? (Enter your answers as a comma-separated list.) t = sec

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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(b) At what time(s) is the height of the ball 52 feet? (Enter your answers as a comma-separated list.) t = [ ] sec
Transcribed Image Text:(b) At what time(s) is the height of the ball 52 feet? (Enter your answers as a comma-separated list.) t = [ ] sec
### Educational Content: Graphing the Trajectory of a Soccer Ball **Problem Statement:** A soccer ball is kicked from 4 feet above the ground. The height, \( h \), in feet of the ball after \( t \) seconds is given by the function \( h = -16t^2 + 64t + 4 \). **Task:** (a) Graph the function. **Explanation of Graphs:** - The graph on the left is a linear plot which rises steadily without any curvature, which might be an incorrect representation for the given quadratic equation. - The graph on the right is a parabolic curve that opens downwards, appropriately depicting the trajectory of the kicked ball. - On the right graph: - The y-axis represents height (\( h \)) in feet. - The x-axis presumably represents time (\( t \)) in seconds, though it isn't labeled. - The parabola reaches a maximum height (vertex) before descending and crossing the y-axis at \( h = 4 \), indicating the initial height when \( t = 0 \). This graph details the expected trajectory of a projectile under the influence of gravity, illustrating the concept of quadratic functions in real-world contexts like projectile motion.
Transcribed Image Text:### Educational Content: Graphing the Trajectory of a Soccer Ball **Problem Statement:** A soccer ball is kicked from 4 feet above the ground. The height, \( h \), in feet of the ball after \( t \) seconds is given by the function \( h = -16t^2 + 64t + 4 \). **Task:** (a) Graph the function. **Explanation of Graphs:** - The graph on the left is a linear plot which rises steadily without any curvature, which might be an incorrect representation for the given quadratic equation. - The graph on the right is a parabolic curve that opens downwards, appropriately depicting the trajectory of the kicked ball. - On the right graph: - The y-axis represents height (\( h \)) in feet. - The x-axis presumably represents time (\( t \)) in seconds, though it isn't labeled. - The parabola reaches a maximum height (vertex) before descending and crossing the y-axis at \( h = 4 \), indicating the initial height when \( t = 0 \). This graph details the expected trajectory of a projectile under the influence of gravity, illustrating the concept of quadratic functions in real-world contexts like projectile motion.
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