Using Vectors to Find Displacement and Angle

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SUMMARY

The discussion focuses on calculating displacement and angle using vector analysis for a person walking a specific path: 4.1 km north, 2.0 km west, and 2.5 km south. The solution involves breaking down the movement into x and y components using basic trigonometry, specifically sine and cosine functions. The final displacement is determined using the Pythagorean Theorem, while the angle is calculated using the inverse tangent function. The user successfully resolved their confusion regarding the reference angles by creating a visual representation of the problem.

PREREQUISITES
  • Understanding of basic trigonometry (sine and cosine functions)
  • Familiarity with vector components and displacement
  • Knowledge of the Pythagorean Theorem
  • Ability to use inverse tangent for angle calculation
NEXT STEPS
  • Study vector decomposition techniques in physics
  • Learn how to apply the Pythagorean Theorem in two-dimensional motion
  • Explore the use of inverse trigonometric functions for angle determination
  • Practice solving displacement problems with varying paths and angles
USEFUL FOR

Students studying physics, particularly those focusing on kinematics and vector analysis, as well as educators looking for practical examples of displacement and angle calculations.

sb13
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Homework Statement


A person walks in the following pattern: 4.1 km north, then 2.0 km west, and finally 2.5 km south.

Homework Equations


(a) How far (in km) and (b) at what angle (measured counterclockwise from east) would a bird fly in a straight line from the same starting point to the same final point?

The Attempt at a Solution


I know that I need to create the triangles for 4.1, 2.0, and 2.5, and use basic trigonometry (sine and cosine) to find the values of each of their x and y components, but I am not sure which reference angles to use 30 degrees, 60 degrees, 45 degrees? How am I supposed to tell? I know where to go from there, you add up all of the x components, and then all of the y components, and then create your final triangle and determine the displacement value using the Pythagorean Theorem. Then you determine the angle by using the inverse of tangent.
I just need help with determining the angles for those three triangles.
 
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Hi sb13,

Make a drawing. Everything will be simple.

ehild
 
Thank you. I figured it out.
 

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