Finding the optimal path across two point with varying speed

In summary, the problem involves finding the optimal path across two points with different speeds for each segment. The equations set up are x/12 + y/4 = P and w + z = 100, but the solver is unsure of how to proceed and is seeking further insight.
  • #1
labyrinthus
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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?
 
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  • #2
I'm still having trouble on figuring out what to do next >.<
 

1. How do varying speeds affect finding the optimal path across two points?

Varying speeds can greatly impact the optimal path between two points. The varying speeds can change the time it takes to reach each point, as well as the distance traveled. This means that the optimal path may not be the shortest or most direct route, but rather a path that balances time and distance based on the varying speeds.

2. What factors should be considered when finding the optimal path with varying speeds?

When finding the optimal path with varying speeds, the most important factor to consider is the speed at which each point can be reached. This can be affected by factors such as terrain, traffic, and mode of transportation. Additionally, the distance between the two points and the desired arrival time should also be taken into account.

3. Is there a mathematical formula for finding the optimal path with varying speeds?

Yes, there are various mathematical formulas and algorithms that can be used to find the optimal path with varying speeds. These include Dijkstra's algorithm, A* search algorithm, and the Floyd-Warshall algorithm. Each of these approaches takes into account factors such as varying speeds and desired arrival time to determine the optimal path.

4. How can technology assist in finding the optimal path with varying speeds?

Technology can greatly assist in finding the optimal path with varying speeds. There are numerous navigation and mapping apps that can calculate the optimal path for a given destination, taking into account varying speeds and other factors. These apps use real-time data and advanced algorithms to provide the most efficient route.

5. Are there any limitations to finding the optimal path with varying speeds?

While there are various methods for finding the optimal path with varying speeds, there are some limitations to consider. These include the accuracy and availability of data, as well as unforeseen obstacles or delays that can affect the varying speeds. It is important to regularly update and adjust the chosen path to account for any changing factors.

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