Finding the optimal path across two point with varying speed

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SUMMARY

The discussion focuses on finding the optimal path between two points, A and C, with varying speeds along segments AB and BC. The speed from A to B is 12 ft/s, while from B to C, it is 4 ft/s. The equations established are x/12 + y/4 = P and w + z = 100, where x represents segment AB and y represents segment BC. The user seeks guidance on progressing from these equations to determine the optimal path.

PREREQUISITES
  • Understanding of basic calculus and optimization techniques.
  • Familiarity with trigonometric functions and their applications in geometry.
  • Knowledge of linear equations and their graphical representations.
  • Ability to interpret and manipulate equations involving speed and distance.
NEXT STEPS
  • Explore optimization techniques in calculus, specifically Lagrange multipliers.
  • Learn about the application of trigonometric functions in pathfinding problems.
  • Investigate the concept of piecewise linear functions in optimization.
  • Study the principles of speed-time-distance relationships in physics.
USEFUL FOR

Students in mathematics or physics, particularly those studying optimization problems, as well as educators seeking to enhance their teaching strategies in calculus and geometry.

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Homework Statement


[PLAIN]http://img214.imageshack.us/img214/194/calcdr.jpg
I need to find the optimal path across two points, in two straight line segments. The speed from point A to B is 12ft/s, and 4ft/s from point B to C.


Homework Equations





The Attempt at a Solution


I set segment AB as x, BC as y, ED as w, and DC as z. With that, I set up the equations:

x/12 + y/4 = P
and
w + z = 100

However, I am stumped at how to progress from here on. I tried playing around with the trigonometric functions in the triangle, but that seemed to complicate the problem even more. Does anyone has any insight into this?
 
Last edited by a moderator:
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I'm still having trouble on figuring out what to do next >.<
 

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