The Canoe Race
A group of canoeists on holiday at the seaside decide to have a race
offshore. They set up a triangular course using a buoy and two other
floats, with the start and finish at the buoy. They have been told
that the prevailing current flows parallel to the shore at a speed of
about 2 ms-1. If the total course is to be 300 metres long investigate
where they might place the other two floats.
Problem: How does the layout of the floats effect the time taken to
complete the race?
I would like to investigate two different models one being a
right-angled triangle and the other being isosceles triangle. When
investigating the isosceles triangle, an equilateral triangle would be
investigated because as the length of the isosceles triangle will all
equal, it becomes an equilateral triangle. I would first of all
investigate the right-angled triangle.
Model 1: Right-Angled Triangle
C
[IMAGE]
A B
[IMAGE]
PREVAILLING CURRENT AT A SPEED OF 2 MS-1
[IMAGE]
COASTLINE
Figure 1: The shape of the course (model 1).
The shape of the course is shown in figure 1. To simplify the problem
I am assuming that the angle CAB is a right angle. Even though the
lengths of B and C will change, angle CAB will always be a right
angle. ‘A’ in figure 1is where the buoy is positioned, and thus it is
the start and finish of the race. The race starts at point A, then it
continues on to point B, then to point C and finishes at the buoy,
which is point A. Point B and C are two floats, first and second float
respectively. I will refer to the lengths AB, BC and AC, throughout
the investigation.
It is more applicable to make assumptions; this would make the problem
simpler. I will use the same assumptions for both the models. It is
vital that we assume that the canoe is a particle and that it’s mass
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