Using calculus to model movement of an object

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SUMMARY

The discussion focuses on using calculus to model the movement of a fly between two trains that are 200 km apart, each traveling towards each other at 100 km/h. The fly, which travels at 200 km/h, repeatedly flies back and forth between the trains until they collide. The solution to the puzzle reveals that the total distance covered by the fly is 200 km, as confirmed by the user Filip. The conversation emphasizes the application of calculus in solving real-world motion problems.

PREREQUISITES
  • Understanding of basic calculus concepts, particularly derivatives and integrals.
  • Familiarity with motion equations and relative speed calculations.
  • Ability to interpret mathematical models and apply them to real-world scenarios.
  • Proficiency in using Excel for modeling and visualizing mathematical problems.
NEXT STEPS
  • Study the principles of calculus related to motion, focusing on derivatives and integrals.
  • Learn how to calculate relative speed in problems involving multiple moving objects.
  • Explore mathematical modeling techniques using Excel for dynamic systems.
  • Investigate similar puzzles and their solutions to deepen understanding of calculus applications in motion.
USEFUL FOR

Students of calculus, educators teaching motion problems, and anyone interested in applying mathematical modeling to real-world scenarios involving relative motion.

musicgold
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Hi,

I am trying to use calculus to analyze the following puzzle. I already know the answer to the puzzle -200Km.
What I want to be able to do is to model or calculate distance the fly travels in a particular sweep. See the attached Excel file to better understand what I mean.

I feel that Calculus might help me in modeling the movement of the fly, but not sure. How should I go about doing this?

Puzzle:
Two trains are 200 km apart, and traveling towards each other at 100 km/hour each. From train A a fly takes off, flying straight above the rails to train B at the speed of 200km/hour, bounces off it and flies back to train A. This is repeated till the trains crash together and the fly is smashed. How much distance does the fly cover?


Thanks.
 

Attachments

Physics news on Phys.org
Thanks a lot Filip.

That is exactly what I was looking for!
 

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