How Do Football Patterns Affect Player Displacement and Angles?

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SUMMARY

The discussion centers on calculating the displacement of a football player running a specific pattern defined by three legs: A (4 meters), B (14 meters), and C (22 meters), with an angle φ of 44° between legs B and C. The player’s displacement magnitude, angle Θ, and the x and y components of the displacement are the primary focus. The problem requires the application of trigonometric principles to derive these values accurately.

PREREQUISITES
  • Understanding of basic trigonometry, including sine and cosine functions.
  • Familiarity with vector components in physics.
  • Knowledge of the Pythagorean theorem for calculating displacement.
  • Ability to interpret geometric diagrams and angles in a physical context.
NEXT STEPS
  • Calculate the magnitude of displacement using the Pythagorean theorem.
  • Determine angle Θ using trigonometric identities.
  • Analyze the x and y components of displacement using vector decomposition.
  • Explore applications of these calculations in sports physics and biomechanics.
USEFUL FOR

Students in physics, coaches analyzing player movement, and sports scientists interested in biomechanics and player efficiency.

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In a practice, a football players runs the pattern shown above. Leg A is 4 meters long, leg B is 14 meters long and leg C is 22 meters long. The angle φ between legs B and C is 44 °. (Legs A and B are perpendicular.) a) What magnitude of the displacement of the football player from her original position?b.)b) What is the value of Θ? c.)C) What is x component of her displacement? (Assume the x direction to be horizontal on that drawing above.)d) What is y component of her displacement? (Assume the y direction to be vertical on that drawing above.)


Picture: https://wug-s.physics.uiuc.edu/cgi/cc/shell/DuPage/Phys1201/fall-evening/tma.pl?Ch-03-04/football_pattern#pr
 
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Hi mai786,

mai786 said:
In a practice, a football players runs the pattern shown above. Leg A is 4 meters long, leg B is 14 meters long and leg C is 22 meters long. The angle φ between legs B and C is 44 °. (Legs A and B are perpendicular.) a) What magnitude of the displacement of the football player from her original position?b.)b) What is the value of Θ? c.)C) What is x component of her displacement? (Assume the x direction to be horizontal on that drawing above.)d) What is y component of her displacement? (Assume the y direction to be vertical on that drawing above.)


Picture: https://wug-s.physics.uiuc.edu/cgi/cc/shell/DuPage/Phys1201/fall-evening/tma.pl?Ch-03-04/football_pattern#pr

Your link appears to require a password. Can you supply a picture somehow else?

Also, remember that you have to show your work on the problem before we can know how to help you.
 
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