SimReal: Exercise - Mathematics - ODE - DiffEq - Boat - Exercise UiA Logo

[SimReal]
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)

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