The football player: Vectors question

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SUMMARY

The discussion focuses on calculating the total displacement of a football player who runs 35 meters down the field and then turns 25 degrees to the right, running an additional 15 meters. The resultant displacement is determined to be 49 meters at an angle of 7.3 degrees to the right of the original direction. Key mathematical tools used include the Pythagorean Theorem and trigonometric functions such as sine, cosine, and tangent to resolve the components of the vectors involved.

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  • Understanding of vector addition and displacement
  • Proficiency in trigonometric functions (sine, cosine, tangent)
  • Familiarity with the Pythagorean Theorem
  • Ability to apply inverse trigonometric functions for angle determination
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  • Learn how to apply the cosine rule for non-right triangles
  • Explore practical applications of trigonometry in sports physics
  • Practice problems involving displacement and direction using real-world scenarios
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1. A football player runs directly down the field for 35 m before turning to the right at an angle of 25 degrees from his original direction and running an additional 15 m before getting tackled. What is the magnitude and direction of the runner's total displacement?

Homework Equations



Pythagorean Theorem (c^2 = a^2 + b^2)
Sin, Cosine, and Tangent Functions
Inverse of Sin, Cosine, and Tangent functions



3. I do not have nay idea how to approach this question. Vectors is an easy concept, but I probably do not understand the context of the question itself. According to the textbook, the answer is "49 m at 7.3 degrees to the right of down-field".
 
Physics news on Phys.org
Th angle between the vectors is 25 degrees. Using cosine rule find resultant displacement.
To find the direction, take the component of 25 degrees along the original direction and perpendicular to the original direction. Using the tangent function find the direction.
 

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