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Boat Landing Problem - Classroom/Home Simulatorand Build your own Simulator by LFS

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?

An interesting problem made accessible for 8th-10th graders using GeoGebra. Try the simulator below or view animated demo.

GeoGebra InterActivity Directions for InterActivity READ ME FIRST!

1. To use: Click and drag input parameters to desired values.

2. Then click the slider point for R (don't drag; you need to see the point glow ). Then you can use arrow keys to find minimum Time.

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 8th-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!

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