How is Swimming and Sinusoidal functions related ?
The swimmer often swims in an circularly interval path which allows the swimmer to train longer in a small swimming pool. The average size of a swimming pool is 25 meters. The shortest race for high school students is 50 meters. When the swimmer dives into the pool, reaches the other side of the pool, and flip turns back and reaches where he or she started; the swimmer has completed one period (cycle). Now, the important aspect is that the speed of the swimmer cannot be constant in all cases. This means that the time that swimmer takes to swim first 5 meters and the turn back cannot be the same, this theory applies to any distance that the swimmer swam. However, the distance of the swimming pool is a constant value. All three aspects of swimming form a periodical, curved sinusoidal graph for us.
1. The distance is constant - 25 meters in length
2. The swimmer's speed is never a constant value, meaning that the time varies.
3. The swimmer is swimming back and forth, which is periodic. (This is an assumption - will explain in the following page!)
For all of the reasons above, a sinusoidal function would be the most appropriate for this scenario.
Myself is a swimmer and have participated in a variety of races. However, My average speed for 50 meters of freestyle is 38 seconds and my fastest speed in a 50 meters freestyle race is 34 seconds.
Swimming is a periodical, and continuous sport.
Here is one of my favorite athlete - Micheal Phelps, breaking a world record in 100 meters butterfly. (optional to watch)
1. The distance is constant - 25 meters in length
2. The swimmer's speed is never a constant value, meaning that the time varies.
3. The swimmer is swimming back and forth, which is periodic. (This is an assumption - will explain in the following page!)
For all of the reasons above, a sinusoidal function would be the most appropriate for this scenario.
Myself is a swimmer and have participated in a variety of races. However, My average speed for 50 meters of freestyle is 38 seconds and my fastest speed in a 50 meters freestyle race is 34 seconds.
Swimming is a periodical, and continuous sport.
Here is one of my favorite athlete - Micheal Phelps, breaking a world record in 100 meters butterfly. (optional to watch)