Football Trajectory Analysis: Coordinates and Interpretation

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Question:

A football is thrown by a quarterback to a receiver. The points in the figure show the height of the​ football, in​ feet, above the ground in terms of its​ distance, in​ yards, from the quarterback. Use this information to solve the problem. Question content area bottom left Part 1 0 6 12 18 24 30 36 42 48 54 60 0 2 4 6 8 10 12 14 Distance of the Football from the Quarterback (yards) Football's Height Above the Ground (feet) x y QB A C D B REC

A coordinate plane has a horizontal x-axis labeled Distance of the Football from the Quarterback in yards from 0 to 60 in increments of 3 and a vertical y-axis labeled Football's Height Above the Ground in feet from 0 to 14 in increments of 1. An arc starts where a point labeled Quarterback throws the ball at (0, 6.3) and ends where a point labeled Receiver catches the ball at (45.6, 6). The arc passes through the plotted points as follows, where the label is listed first and the coordinates of the point are listed second: A, (3, 8); C, (9, 10.6); D, (36, 10.6); B, (42, 8). All coordinates are approximate. . . . Question content area right Part 1 Find the coordinates of point Upper A.    enter your response here ​(Type an ordered pair. Type integers or decimals rounded to the nearest tenth as​ needed.) Part 2 Interpret the coordinates. When the ball has traveled a distance of    enter your response here ▼ meters, feet, yards, it is at a height of    enter your response here ▼ meters. feet. yards.​(Type integers or decimals rounded to the nearest tenth as​ needed.)

Answer:

To solve the problem, we need to find the coordinates of point A and interpret them.

Part 1: Find the coordinates of point A.

From the information provided, point A is given as (3, 8). This means:

  • The x-coordinate (distance from the quarterback) is 3 yards.
  • The y-coordinate (height of the football) is 8 feet.

So, the coordinates of point A are: (3, 8)

Part 2: Interpret the coordinates.

The coordinates (3, 8) can be interpreted as follows:

  • When the ball has traveled a distance of 3 yards, it is at a height of 8 feet.

Final Answers:

Part 1: (3, 8)

Part 2:

  • When the ball has traveled a distance of 3 yards, it is at a height of 8 feet.