Boat Landing Problem- Classroom/Home Simulator and 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: A 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!

Boat Landing ProblemProblem 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:A 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 InterActivityDirections for InterActivityREAD 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.InterActive web page with Good Questions and more ...Metadata(includes links for downloads)More Resources for this ProblemRelated Topics:4.1 Polynomials -> Box Folding Problemboat, landing, interactivity, extreme, minimum, velocity distance, time, speed, geogebra, application, geometry, program