Set d, the horizontal starting distance between the turtle at A and the turtle at B, in the slider. Click on the green flag. To learn about the origin of the problem and the mathematics underlying the project see Notes and Credits below.
This problem appeared in the September 2012 issue of The Physics Teacher. Two turtles, A (green) and B (yellow), are relaxing at the water's edge a distance 'd' apart. Then turtle A begins to swim away from the shore. Turtle B gives chase, taking off at the same moment. During the chase A keeps swimming directly away from the shore while B keeps swimming directly towards A. The speeds of both turtles are the same. Find the distance between A and B after a long time interval. When I read the problem I thought, "I don't have to solve the problem algebraically (or by using calculus), I can 'model' it in Scratch!" Once the yellow turtle is vertically 'behind' the green turtle, the separation distance is approximately d/2. The project allows one to form a 'conjecture' that can be proven or disproven mathematically. In mathematics, curves of this type are called pursuit curves. See my 4-Bug Scratch project at https://scratch.mit.edu/projects/339999/ for another example of a pursuit curve. Credit: I replaced the original turtles in this project with the 'Urbino Turtles' from the project Shared by breenworks. View this project at: https://scratch.mit.edu/projects/100041049/
