Relative velocity and distance between particles

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SUMMARY

The discussion focuses on calculating the shortest distance between two particles, A and B, given their lengths L₁, L₂ and velocities V₁, V₂. The solution involves deriving the distance function as a function of time and applying the cosine rule to determine the relationship between the particles. To find the minimum distance, participants recommend taking the first derivative of the distance function and solving for the time at which this minimum occurs. This approach allows for the calculation of the minimum distance by substituting the time back into the distance function.

PREREQUISITES
  • Understanding of relative velocity concepts
  • Familiarity with calculus, specifically differentiation
  • Knowledge of the cosine rule in geometry
  • Ability to formulate distance functions based on particle motion
NEXT STEPS
  • Study the application of the cosine rule in physics problems
  • Learn how to derive distance functions for moving objects
  • Explore optimization techniques in calculus for finding minima
  • Investigate relative motion and its implications in particle dynamics
USEFUL FOR

Students studying physics, particularly those focusing on kinematics and particle motion, as well as educators looking for effective methods to teach these concepts.

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Homework Statement



Lengths L₁, L₂. Velocities V₁, V₂.

Homework Equations



Find the shortest distance between particle A and B.

The Attempt at a Solution



[I seriously don't have any clue how to start this question itself.
 

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You sholud first find the distance between the two given objects as a function of time. I'm not sure if [itex]\theta[/itex] in your picture is [itex]90^{\circ}[/itex] angle or not, but cosine rule will definitely work.

Then you find the first derivative of that function in order to find the time at which the distance is minimum. When you got that time, it's easy to find the distance by plugging it back to the distance function.
 

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