The height y (in feet) of a punted football is approximated byy = − (16/2025) x2 +(9/5)x+(3/2)where x is the horizontal distance (in feet) from the point at which the ball is punted. (See figure.) (a) Use a graphing utility to graph the path of the football. (b) How high is the ball when it is punted? (Hint: Find y when x = 0.)_____________ ft(c) What is the maximum height of the football? (Round your answer to two decimal places.)____________ ft(d) How far from the punter does the football strike the ground? (Round your answer to two decimal places.)__________ ft from the punter This image illustrates a projectile motion scenario on a football field. A football is kicked by a player, following a curved trajectory. The trajectory is shown as a parabolic arc. The player is positioned near the 50-yard line on the field. The flight path of the football crosses several yard lines, with the horizontal distance from the starting point labeled as "x." The highest point of the trajectory is marked with a vertical distance labeled "y," representing the maximum height the football reaches. The diagram includes elements of a stadium, such as empty bleachers and stadium lights. In the background, there are buildings and trees, giving a sense of an outdoor sports setting. The image has a note: "Not drawn to scale," indicating that the proportions in the diagram may not represent real-life measurements. This visual is useful for illustrating principles of physics, such as projectile motion, gravity, angles of launch, and the parabolic path of objects in motion.

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Answered: The height y (in feet) of a punted…

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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Question

The height y (in feet) of a punted football is approximated by

y = − (16/2025) x²+(9/5)x+(3/2)

where x is the horizontal distance (in feet) from the point at which the ball is punted. (See figure.)

(a) Use a graphing utility to graph the path of the football.

(b) How high is the ball when it is punted? (Hint: Find y when x = 0.)
_____________ ft
(c) What is the maximum height of the football? (Round your answer to two decimal places.)
____________ ft
(d) How far from the punter does the football strike the ground? (Round your answer to two decimal places.)
__________ ft from the punter