Distance and height of cannon projectiles For mathematical investigation, I want to focus on angles, trigonometry and differentiation, as these areas are the ones that interest me the most more in the SL program, and relate it to the history of war and weapons used in wars, which are some of my other interests. I teach history at a higher level at IB and war has always been an interest of mine. The cannon has improved over the past 1000 years and is an effective way for an army to fire a long-range projectile at an enemy fortress. or behind enemy walls. But did the angle at which the cannons were fired have any effect on how far the projectile traveled, and were the soldiers manning the cannons aware of the angle that would move the projectile furthest and be most accurate? occurred in the 19th and 20th centuries, it is quite possible that the soldiers cocking and firing the cannon did not have the proper training to maximize their accuracy. An example of this is the American Civil War, where soldiers could have used "trial and error" methodology, i.e. shoot once at a certain angle, see where it lands, and change the angle based on the distance to the target. I began to think about how awareness of the correlation between speed and firing angle could affect the effectiveness of the army, since it would have to fire less and thus save time and money . So, study how different guns, with different velocities, could provide an advantage to the soldiers. Additionally, using calculus, I will study the maximum distance of different guns used during the war. So the question I want to explore is whether in applying trigonometry a middle of paper ......r should do is look at the curve of the barrel they are using and find out what angle would be optimal. to hit an enemy at a certain distance.Graph 3: The effect of angle on distance, using the equation found previously shown on three different guns, with three different velocitiesWorks Cited Model 1841 6-Pounder (Gun) Towed Field Gun. Military factory, nd Web. April 9, 2014. .Poduct Rule for Derivatives. HMC, and Web. April 9, 2014. .Projectiles. University of Plymouth, nd Web. April 9, 2014. .Range of an artillery shell. Physics Factbook, nd Web. April 9. 2014. .