What is the Magnitude of Displacement for Various Directions and Distances?

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SUMMARY

The discussion focuses on calculating the magnitude of displacement for various scenarios using vector addition principles. The first problem involves a car traveling 125 km west and 65 km south, resulting in a displacement of approximately 140.9 km. The second problem calculates a shopper's displacement of about 257.1 m after walking 250 m and then 60 m at a right angle. The third problem involves a hiker's displacement of approximately 4.526 km after walking 4.5 km and then 6.4 km at a 45-degree angle. The fourth problem remains unresolved, with users discussing the combination of equations to find the resultant displacement.

PREREQUISITES
  • Understanding of vector addition and displacement
  • Familiarity with the Pythagorean theorem
  • Knowledge of trigonometric functions, specifically cosine
  • Ability to solve problems involving angles and resultant vectors
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  • Study the application of the Pythagorean theorem in vector problems
  • Learn how to use the law of cosines for non-right triangles
  • Practice calculating resultant vectors from multiple directions
  • Explore real-world applications of displacement in physics
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Students in physics courses, educators seeking clarification on vector displacement, and anyone interested in mastering vector addition and displacement calculations.

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Okay i don't have the best physics teacher :-/ he often gets confused with what he's teaching and shows us the wrong thing...We have four problems for homework and I would just like one of you experts to check over it ;)

1. A car is driven 125 km due west, then 65 km due south. What is the magnitude of displacement? R^2=a^2 + b^2
R^2=125^2 + 65^2
R^2=19850
R=140.9 (about)
2. A shopper walks from the door of the mall to her car 250m down a lnae of cars, then turns 90 degrees to the right and walks an additional 60m. What is the magnitude of the displacement of her car from the mall door?
R^2=a^2 + b^2
R^2=60^2 + 250^2
R^2=66100
R=257.1 (about)
3. A hiker walks 4.5 km in one direction, then makes a 45 degree turn to the right and walks another 6.4 km. What is the magnitude of her displacement?
R^2= a^2 + b^2 - 2ab COS(angle)
R^2= 4.5^2 + 6.4 ^2 -2(4.5)(6.4)cos45
R^2=20.25 + 40.96- 40.729
R^2=20.481
R=4.526 (about)
4. What is the magnitude of your displacement when you follow directions that tell you to walk 225 m in one direction, make a 90 degree turn to the left and walk 350 m, then make a 30 degree turn to the right and walk 125 m?
I'm not sure how to go about doing this one but what I DO know is
how the triangle looks and the angle measurements. I'm just not
sure what it is I'm supposed to be writing down. A hand please lol?
 
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...would I use the first or second equation? What about a combination of both? ...maybe its a trick question lol maybe its right there you just have to know what it is...
 
You could use both. Get the resultant magnitude (R1) from the first two directions. And then find the resultant (R2) from R1 and the 3rd vector.
 
thanks! is the rest of it right?
 
isnt the resultant vector 125? whoaaa...*confused*
 
To find the resultant magnitude I would use r2=a2+b2 rite? i don't know what youre talking about the next part that confuses me..3rd vector is 125 correct?
 
please someone help my gpa is plummeting thru tha ground I've made 2 awful homework grades recently: 71% and a 76%! :'(
 

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