SimReal: Exercise - Mathematics - ODE - DiffEq - Boat - Exercise | ![]() |
![]() |
A boy, standing in corner A of a rectangular pool, has a boat in the adjacent corner B on the end of a string 10 meters long. He walks along the side of the pool toward C keeping the string taut. Describe the motion of the boat. Locate the boy and the boat when the latter is 6 meters from the line AC. Hint: 01: Do the experiment in real. What will influence the result of the experiment? 02: Do a simulation of the experiment in the classroom. What will influence the result of this simulation? 03: If you have done both point 1 and point 2, what is the conclusion when you compare those two experiment? 04: Construct a mathematical model of the task. 05: Find a numerical solution of the mathematical model using a digital tool. 06: Compare the numerical solution in point 5 with the result from point 1 or 2. 07: Find an analytical solution of the mathematical model. 08: Compare the numerical and the analytical solution. 09: Program a simulation of the mathematical model in Python and SimReal. 10: Do an overall conclusion of this exercise. |
Simulate this experiment by the help of small object (boat), pen and paper on a horizontal area. Mark 10 points on the path of the boat. Especially notice the point when the boat is 6 m from the horizonal line from A. Notice how far from the verical line AB the boat is now and at what position E the boy is right now. Describe by a mathematical model (differential equation) the path (red color) that the boat will follow. Use the SimReal-application above to: - Input the mathematical model - Find the numerical solution of the path - Draw the graph - Simulate the movement of the boat - Find out how far from the vertical line the boat is when the boat is located 6 m from the horisontal line AE - What is the position of the point E (boy with the rope) now? - Compare the result from the experiment and from the mathematical model SimReal - Interactive tool SimReal - Solution (SimReal is more flexible and interactive than Python) Python - Solution (Python is more easy to program than SimReal) |