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:Ь The shoreline is straight. Ь The current flows in a fixed direction (i.e. it will not change) Ь Canoeists take no time to turn Ь The canoeists do not tire (i.e. their speed is constant) Ь The canoeists start the race at their constant speed (i.e.: 4ms-1) Ь 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. ?