Football Pattern Vectors Question

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Homework Help Overview

The problem involves calculating the x and y components of a football player's displacement based on the lengths of three legs of a path and the angle between two of them. The context is rooted in vector analysis and trigonometry.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to calculate the x and y components of displacement using trigonometric functions based on the given lengths and angles. Some participants question the setup regarding the perpendicularity of legs A and B and the angle measurement.

Discussion Status

Participants are actively discussing the calculations, with some pointing out potential errors in the original poster's approach. There is a suggestion to clarify the geometric relationships and the use of trigonometric functions. A visual aid has been provided to enhance understanding.

Contextual Notes

There is a noted confusion regarding the angle between legs A and B, as well as the implications of the angle φ on the calculations. The original poster expresses uncertainty about their results, particularly for the y component of displacement.

vane12
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In a practice, a football players runs the pattern shown above. Leg A is 3.0 meters long, leg B is 13.0 meters long and leg C is 23.0 meters long. The angle φ between legs B and C is 38.0°. (Legs A and B are perpendicular.)

1.)What is x component of her displacement? (Assume the x direction to be horizontal on that drawing above.)
(A+B+C)x =
2.)What is y component of her displacement? (Assume the y direction to be vertical on that drawing above.)
(A+B+C)y =

For to find the x and y component I did the following:

Ax=3cos0°=3
Bx=13cos38°=10.24
Cx=23cos(-38°)=18.12

Ay=3sin90°=3
By=13sin38°=8.00
Cy=23sin(-38°)=-14.16


(A+B+C)x=31.336 which I got correct but for (A+B+C)y=-3.16 which I didn't get correct and I don't know what I did wrong??
 
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Welcome to PF.
I'm a bit confused how leg A and B are perpendicular but there is only a 38 deg angle difference between the two. For Ay you have 3sin90 but for Ax you have 3cos0?
Seems that your Ay is incorrect since you got part 1.
In the future illustrations go a long way.
 
Here is a picture.
 

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    football pattern.gif
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By = 0
 

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