Home > Do Mathematics -> Algebra 1 -> 4. Polynomials -> Boat Landing Problem

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 vr and walks with a speed of vw . 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 red for R (don't drag; you need to see the point glow red_glow). Then you can use arrow keys to find minimum Time.

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Good Questions InterActive Webpage
Metadata (includes links for downloads)
Global Quadratic Functions
Brief InterActivity-Simulator for the Folding Box Maximum Value Problem
Grade 8th and up (Graphic Solution); Calculus (Algebraic Solution)
Strand Graphic Solution: Algebra 1   Algebraic Solution with Derivatives: Calculus
Standard Algebra 1 4.1 or Algebra 1 5.7 or AP Calculus 11
Keywords function, equation, boat landing, extrema, extreme values, calculus, dynamic, freeware, applet, offline, online
Worksheet Worksheet with Problems and Questions
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 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!
Online Online Activity
Download Downloads: School LAN Version Zip  Completely Offline Version  
Author LFS - contact
Type Freeware - Available for Offline and Online Use - Translatable (html)
Use Requires sunJava player
More Resources for this Problem 

Related Topics: 4.1 Polynomials -> Box Folding Problem

boat, landing, interactivity, extreme, minimum, velocity distance, time, speed, geogebra, application, geometry, program