Direction of resulting displacement

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SUMMARY

The discussion focuses on calculating the direction of resulting displacement in a multi-segment route. The key equation used is displacement = final velocity - initial velocity, with an emphasis on converting radians to degrees using the formula x180/pi. The angle DAB, representing the displacement direction, is determined by constructing a right triangle and applying the cosine function to find the relationship between the distances AD and AE. The visual representation through a diagram is crucial for understanding the geometric relationships involved.

PREREQUISITES
  • Understanding of basic trigonometry, specifically cosine functions
  • Familiarity with vector displacement concepts
  • Knowledge of angle conversion from radians to degrees
  • Ability to interpret and create geometric diagrams
NEXT STEPS
  • Study trigonometric identities and their applications in physics
  • Learn about vector addition and displacement in physics
  • Explore the concept of right triangles and their properties
  • Practice problems involving angle conversion and displacement calculations
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and vector analysis, as well as educators looking to clarify concepts of displacement and direction in multi-segment paths.

jamiebean
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Homework Statement
attached below:
Relevant Equations
displacement=final velocity-initial velocity
螢幕截圖 2020-05-21 下午12.57.17.png
螢幕截圖 2020-05-21 下午12.57.31.png


I do not understand part b.
I know that x180/pi changes the value into a degree, but i do not understand what's going on inside the bracket. And how did the equation calculated the direction?
 
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jamiebean said:
Homework Statement:: attached below:
Relevant Equations:: displacement=final velocity-initial velocity

View attachment 263178View attachment 263179

I do not understand part b.
I know that x180/pi changes the value into a degree, but i do not understand what's going on inside the bracket. And how did the equation calculated the direction?
Suppose the route goes from A north to B, west to C, then south to D.
Draw the diagram.
The angle you want is DAB. That is how much west of north the displacement is.
Now draw a line East from D until it hits the line AB at E. What is the distance AE? You already have the distance AD.
In terms of those, what is the cosine of DAB?
 
haruspex said:
Suppose the route goes from A north to B, west to C, then south to D.
Draw the diagram.
The angle you want is DAB. That is how much west of north the displacement is.
Now draw a line East from D until it hits the line AB at E. What is the distance AE? You already have the distance AD.
In terms of those, what is the cosine of DAB?

thank you! I understand now!:))
 
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