Projectile Motion in Archery

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Archery, a sport that dates back to centuries before today, has been modernized to become more efficient and high tech. The Egyptian made the first complex bow in 2800 BC. The bow was made from sheep intestines and the arrow was light and efficient enough to be shot from 400 yards away and still penetrate the armor used at that time. Archery was a skill set that was prized in the military, especially in Rome. However, in 16th century a new tide was turning in Europe, firearms were slowly replacing the bow and arrow as military weapons. Other parts of the world were not as fast to leave behind archery this weapon. The people of the Far East employed archery in warfare until the 19th century, while people in Central and South Africa still use it to this day for hunting and intertribal fighting. Archery, in many parts of the world today, is viewed by some as a recreational sport and by others, as a competitive sport. Due to this, the shapes of the bow and the arrow have gone through many changes since the first model of the bow and arrow.
The three main types of bows today are the recurve bow, the compound bow, and the longbow. In addition to this, there are also three types of arrows the carbon arrow, aluminum arrow, and wooden arrow. Due to the different types of materials, the distance one shot covers is relative to each bow and arrow.
In order to shoot an arrow, one needs to think about their target and what angle is most appropriate to shoot from. There are a lot of factors to keep in mind when doing this. Such as the velocity of your arrow, the optimal height you want, and the distance you want to cover. In my exploration, I wanted to see how the different aspects of projectile motion would affect the compound bow and the conve...

... middle of paper ...

...arrow to reach optimal height and back down. Once I got the value of the gravity, I found that it would be helpful in figuring out the time (t) that it takes the arrow to reach its optimal height and back down to the ground. The equation I used to figure this out was v=u+a(t), v being the final velocity, u being the initial velocity, and a being the acceleration. I then replaced a(t) with g(t) since gravity (g) is a constant value. I did this because gravity has no effect on horizontal velocity, but speeds and slows down the vertical velocity. The regular equations for acceleration in both horizontal and vertical velocities are ax=0 and ax=-g. So I decided that I would use a 45° angle as my reference angle, since it achieves the greatest range.

Compound Bow Conventional Longbow
0=59.255818m/s−9.78m/s2

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