Problem setting: A man with a boat at point S at sea wants to get to point Q inland. Point S is distance d1 from the closest point P on the shore, point Q is distance d2 from the closest point T on the shore. The points P and T are at a distance of d from each other.

 

Question: If the man rows with a speed of v_r and walks with a speed of v_w at what point R should he beach the boat in order to get from point S to point Q in the least possible time?

 

 

 

Activities:

 
1. Play with ready-to-use simulation.   See animated demo!

 
2. Some Good Questions for this activity.
 
3. Build your own simulator   Complete mathcast(av) demo!

 
  Download simulator for offline use.
 
  Download pdf directions for building simulator.
 
  Download starter file for offline build. Build Simulator Online!

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Level: 10th grade and up (later for AP Calculus - Extreme Value/Numerical Approximations)  
Goal: Real Problems - Real Simulations (later Real Solutions)
Comments: This is an interesting problem - it requires only Pythagoras' theorem and distance-rate-time formula to set up and run a simulation. It is easy to understand different aspects of it and to have many discussions. Good for 10th grade. Then later in AP Calculus, one can move to the actual "mathematical solution", which is an extreme value problem also with wide ranging discussions!
Requires: SunJava Player for Interactivities, Flash Player for Demos, GeoGebra for offline simulation
Author: Linda Fahlberg-Stojanovska

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Page last modified on April 06, 2010, at 12:04 PM