The Canoe Race Investigation Essay, Research Paper

Introduction:??????????? The canoe

race investigation aims to explore the relationship between the dimensions of a

canoeing course (comprising one fixed buoy and two other floats) in the sea,

with a current of 2ms-1?parallel to the shore; which has

a total distance of 300m.? I have chosen

to investigate the relationship combining dimensions and time ? ultimately

trying to find the quickest course.Simplified Assumptions:??????????? To make the

investigation easy to comprehend I have made the following assumptions that

will not be changed over the course of the investigation:Ü The

shoreline is straight. Ü The

current flows in a fixed direction (i.e. it will not change) Ü Canoeists

take no time to turn Ü The

canoeists do not tire (i.e. their speed is constant) Ü The

canoeists start the race at their constant speed (i.e.: 4ms-1) Ü Apart

from the current the water is still (i.e. there are no waves)The Model:??????????? There are

many different types of circuit that the canoeists can use. Equilaterals,

isosceles, right angled triangles and many others, including a straight course

where the canoeists have to travel up one side and back down the other.? All of these shapes can be altered to

incorporate the direction of the current and the length of the side that is

parallel to the shoreline.? I will also

investigate whether clockwise and anticlockwise have any major differences in

time.? ??????????? In all

cases the length of sides A + B + C = 300m.?

\The

formula that I will use for calculating the total time taken is => (length A

/ res. velo) + (length B/ res. velo) + (length C / res. velo).??????????? Res. Velo =

resultant velocity, which is attained from the diagrams that I will draw.Equilateral Triangles:??????????? This first

equilateral triangle has a side length of 100m parallel to the shore. The time

taken for the clockwise circuit is 112.5 seconds. ??????????? However,

the time taken for the anticlockwise circuit is 104.86 seconds.? It is clear from this that there is no

considerable difference in time between the directions of travel.? I will therefore concentrate on the

clockwise circuits of isosceles triangles.Isosceles triangles:??????????? ? The isosceles triangle will be a more

beneficial shape for the canoeists to use because they can decrease the length

of the side where they travel parallel to the shore (i.e. against the current).Isosceles (base = 90) => 108.75 seconds Isosceles (base = 80) => 105 secondsGraphical interpretation??????????? A graph can

be drawn, showing the relationship between the shore side length and the time

taken to complete the circuit.? From the

above results we can expect the relationship to be directly proportional.??????????? To save

time I have calculated the times taken for each base length without drawing the

diagram.? The time taken for the longer

sides will always be 4ms-1 and the speed against the current will

always be 1.6ms-1.? The base

length of 150m represents the circuit that is all three buoys in a straight

line parallel to the shore (speed for this is 5.6ms-1 with the

current and 1.6ms-1 against it). Base Length (m) Time (seconds) 150 120.53 100 112.5 90 108.75 80 105 70 101.25 60 97.5 Conclusion:??????????? As the base

length increases the time taken to complete the circuit also increases.? This is due to the fact that when the

canoeists are travelling in a clockwise direction, the slowest leg of the

circuit when paddling against the current.?

Therefore it makes sense that the quickest time is when the shortest

time is spent against the current.Improvements:??????????? Should I

repeat this model I would improve the following points to make the model more

accurate:? Canoeists tire.? This would make certain parts of the circuit a lot slower and

would require real data from experiments carried out. ? The race was meant to take place in the sea ?

waves, tide and wind would affect the speed of the canoeists. ? Time is taken to turn the corners ? again

experimental data would be required ? Sine/Cosine rule could be used to make the

calculations more detailed and improve accuracy. ? Canoeists take time to reach their maximum

speed ? i.e. there is no ?rolling start? ? Age and sex of the canoeists in the race may

play an important factor in speed. ? Height and Weight may also affect the speed

of each competitor. ?