Resultant Displacement with direction problem

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SUMMARY

The discussion centers on calculating resultant displacement and total distance traveled during a running scenario. The participant calculated a total running distance of 2160 meters by converting time into seconds and multiplying by velocity. However, they struggled with determining the resultant displacement, attempting to use trigonometric methods with a 45-degree angle for the northeast direction but did not arrive at the correct answer. The key takeaway is the importance of accurately breaking down vector components when calculating resultant displacement.

PREREQUISITES
  • Understanding of basic kinematics, including distance, speed, and time calculations.
  • Familiarity with vector components and how to resolve them using trigonometry.
  • Knowledge of angles, specifically 45-degree angles in relation to directional movement.
  • Ability to convert units of time from minutes to seconds for calculations.
NEXT STEPS
  • Study vector addition and how to calculate resultant displacement in two dimensions.
  • Learn about resolving vectors into horizontal and vertical components using trigonometric functions.
  • Practice problems involving kinematic equations and vector components to reinforce understanding.
  • Explore graphical methods for vector addition to visualize resultant displacement.
USEFUL FOR

Students studying physics, particularly those focusing on kinematics and vector analysis, as well as educators looking for examples of displacement calculations in real-world scenarios.

pennywise1234
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Homework Statement


You run towards the west with a velocity of 4 m/s for 5 minutes. You then continue running to the northeast (halfway between north and east) at 2 m/s for 8 minutes. (a) At the end of the 13 minute run , what was your total running distance? (b) At the end of the 13 minute run, what was your resultant displacement relative to your starting position?

Homework Equations


trig

The Attempt at a Solution


i got the total distance by converting minutes into seconds and multiply the number by each velocity i got 2160m for total running distance. i was unable to figure out the resultant i created the triangle with using 45 degrees as the angle (due to the north east reference), but i am not getting the answers similar to the answer keyi used the given numbers to find the vertical and horizontal components so i made my triangle with the 45 degree reference and 2m/s to find the horizontal and vertical components (i solved using trig) that did not due.i then tried using the numbers converted to seconds and that did not work either. So i used 960m/s to solve the triangle with the 45 degree reference . As that is the number you get when you multiple 2x60x8. I am also including the 4 or 1200(when multiplied) as an added horizontal component and did not get the right answer

where did i got wrong
 
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pennywise1234 said:
where did i got wrong
No way to tell if you do not post your working.
 

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