Aesop’s Fables Folio
A 600-metre race is conducted between the cat, dog and hedgehog to determine which animal can run the distance the fastest. The aim of the investigation is to identify the characteristics of animals’ races and in the final analysis, the results of the initial, semi-final and gold medal races. The cat follows a quadratic line with the equation . The dog’s path follows a cubic line with the equation . The hedgehog follows a linear path with the equation . These graphs can be seen below. A graphics calculator will be used for finding roots of polynomials for specific questions and desmos.com is used to graph the models for each animal.
Cat
Dog
Hedgehog
The hedgehog has a head start of 50 metres. The head start is found …show more content…
The biggest strength of the hedgehog is the fact that it will move at a constant rate for a race of an infinite distance. Even if the hedgehog was not given his head start of 50 metres he would have won the 600-metre race. The cat is much better at running shorter distances and it could receive a higher place if it was a short race. The closer that the cat runs to its turning point the slower its pace and it cannot run more than 625 metres. The finish line was placed in a position close to cat’s vertex meaning that cat was running slowly towards the end of the race. The dog would have easily won if the race was shorter or longer because its speed is far superior to the other animals. If the race was 550 metres, for example, the dog would have completed the race before becoming distracted by the bone. If it was 760 metres the dog’s speed would have resulted in him outrunning his opponents.
Some race distances that could have given each animal individually a significant advantage.
Hedgehog
558-755 metres – the other animals are given the most disadvantage at that point as they are influenced by the presence of a turning point. The hedgehog is linear and is not affected by …show more content…
Hedgehog is waiting at the y-intercept of its graph (0, 50) - at the 50-metre mark. Both the dog and cat are waiting for the beginning of the race at (0, 0). The race begins and the dog has a very good start, it has been only 15 seconds and he is already in first place. The race began two minutes ago and as I speak hyena is beginning his race, but at a slow pace as he is close to his vertex at (-5, -49). Cat encounters hedgehog at (5, 225) and is in second place. It’s 5 minutes in and it looks like dog will easily win the race, but he seems to be rapidly slowing down. Dog is at the coordinate (5.381, 557.069) when he turns around. On dog’s return he first encounters cat at (9.576, 387.087) and then immediately after he meets hedgehog at (9.595, 385.835). The placings now are Cat, Hedgehog, Dog, Hyena. Cat is now slowing down and meets hedgehog again 10 minutes into the race at (10, 400). Hyena meets his first opponent of the race, dog, at (12, 240) and moves up to 3rd position. Dog digs up his bone at (14.619, 162.931) and heads toward the finish line, slowly building up his pace. Hyena is gradually gaining pace further into the race but cat is slowly losing its speed as it approaches is vertex at (25, 625). Dog and hyena meet one last time before completing the race at (19.105, 532.036) and directly before finishing dog and cat intersect at (19.424, 593.913). Hedgehog receives first place for crossing the finish
A 600-metre race is conducted between the cat, dog and hedgehog to determine which animal can run the distance the fastest. The aim of the investigation is to identify the characteristics of animals’ races and in the final analysis, the results of the initial, semi-final and gold medal races. The cat follows a quadratic line with the equation . The dog’s path follows a cubic line with the equation . The hedgehog follows a linear path with the equation . These graphs can be seen below. A graphics calculator will be used for finding roots of polynomials for specific questions and desmos.com is used to graph the models for each animal.
Cat
Dog
Hedgehog
The hedgehog has a head start of 50 metres. The head start is found …show more content…
The biggest strength of the hedgehog is the fact that it will move at a constant rate for a race of an infinite distance. Even if the hedgehog was not given his head start of 50 metres he would have won the 600-metre race. The cat is much better at running shorter distances and it could receive a higher place if it was a short race. The closer that the cat runs to its turning point the slower its pace and it cannot run more than 625 metres. The finish line was placed in a position close to cat’s vertex meaning that cat was running slowly towards the end of the race. The dog would have easily won if the race was shorter or longer because its speed is far superior to the other animals. If the race was 550 metres, for example, the dog would have completed the race before becoming distracted by the bone. If it was 760 metres the dog’s speed would have resulted in him outrunning his opponents.
Some race distances that could have given each animal individually a significant advantage.
Hedgehog
558-755 metres – the other animals are given the most disadvantage at that point as they are influenced by the presence of a turning point. The hedgehog is linear and is not affected by …show more content…
Hedgehog is waiting at the y-intercept of its graph (0, 50) - at the 50-metre mark. Both the dog and cat are waiting for the beginning of the race at (0, 0). The race begins and the dog has a very good start, it has been only 15 seconds and he is already in first place. The race began two minutes ago and as I speak hyena is beginning his race, but at a slow pace as he is close to his vertex at (-5, -49). Cat encounters hedgehog at (5, 225) and is in second place. It’s 5 minutes in and it looks like dog will easily win the race, but he seems to be rapidly slowing down. Dog is at the coordinate (5.381, 557.069) when he turns around. On dog’s return he first encounters cat at (9.576, 387.087) and then immediately after he meets hedgehog at (9.595, 385.835). The placings now are Cat, Hedgehog, Dog, Hyena. Cat is now slowing down and meets hedgehog again 10 minutes into the race at (10, 400). Hyena meets his first opponent of the race, dog, at (12, 240) and moves up to 3rd position. Dog digs up his bone at (14.619, 162.931) and heads toward the finish line, slowly building up his pace. Hyena is gradually gaining pace further into the race but cat is slowly losing its speed as it approaches is vertex at (25, 625). Dog and hyena meet one last time before completing the race at (19.105, 532.036) and directly before finishing dog and cat intersect at (19.424, 593.913). Hedgehog receives first place for crossing the finish