WAR MATHS- PROJECTILE MOTION
Sun Tzu, the man whose name is famed by the phrase, the art of war, once said “Victorious warriors win first and then go to war, while defeated warriors go to war first and seek to win. ” which means victors were the ones who calculated and analyzed their opposition and factors that would ensure their victory. Cannons and catapults in my view, were the earliest form of artillery used for fighting wars with great separation distances between the parties at war. Bows and Arrows also were sure to level the battlefield if the enemies were caught unaware, securing a victory in war without swords engaging. The concepts or methods of fighting required a parabolic trajectory launch to fly a greater distance and reach the …show more content…
My view on the aim of this projectile motion which I would say it’s simple but ingenious is that, objects at launch were able to be fired at a long distance depending on the power, angle and initial velocity at launch hence in a war, it did not have to engage and commence with swords but could begin by both sides firing their artillery at a distance. Even for the battle in sports, players do not have to be close to aim for a goal as long as enough power is applied. Projectile motion, as the motion of an object under the effect of gravity with a downward magnitude g = 9.80m/s2 (assumed constant), perceived as not being affected the air resistance . For a motion of any object that follows the parabolic motion, there are vertical and horizontal vector components that can be analyzed to further understand this two dimensional motion. There are two types of projectile motion; a projectile launched horizontally from the top of a tall building or a cliff and a projectile that is launched at an angle from the ground. In both types, it should be noted that along the horizontal, there is no force acting and so there is no acceleration in that direction hence motion will stay constant (due to air resistance being ignored), whereas in the vertical direction there is acceleration because of the existence of force of …show more content…
The picture below will present my intended study of projectile motion in the battle. Consider: A castle that is 3,000 metres away To destroy the castle, the cannon would have to hit precisely about the point B from point A. Muzzle velocity of a cannon = 120m/s to 390m/s (but I will use the average velocity to cater for the large indifference) Force of gravity g = 9.81m/s2 Angle (°degrees) Range (m)
X= (V_0^2 sin2θ)/g Maximum height (m) h=(v_0^2 sin〖θ sinθ 〗)/2g Deviation from the range of 3000m
0 0 0 0
30 5740 829 +2740
45 6628 1657 +3628
60 5740 2485 +2740
90 0 3314 -3000
15 3314 222 +314
14 3112 194 +112
13 2906 168 -94
12 2696 143
Sun Tzu, the man whose name is famed by the phrase, the art of war, once said “Victorious warriors win first and then go to war, while defeated warriors go to war first and seek to win. ” which means victors were the ones who calculated and analyzed their opposition and factors that would ensure their victory. Cannons and catapults in my view, were the earliest form of artillery used for fighting wars with great separation distances between the parties at war. Bows and Arrows also were sure to level the battlefield if the enemies were caught unaware, securing a victory in war without swords engaging. The concepts or methods of fighting required a parabolic trajectory launch to fly a greater distance and reach the …show more content…
My view on the aim of this projectile motion which I would say it’s simple but ingenious is that, objects at launch were able to be fired at a long distance depending on the power, angle and initial velocity at launch hence in a war, it did not have to engage and commence with swords but could begin by both sides firing their artillery at a distance. Even for the battle in sports, players do not have to be close to aim for a goal as long as enough power is applied. Projectile motion, as the motion of an object under the effect of gravity with a downward magnitude g = 9.80m/s2 (assumed constant), perceived as not being affected the air resistance . For a motion of any object that follows the parabolic motion, there are vertical and horizontal vector components that can be analyzed to further understand this two dimensional motion. There are two types of projectile motion; a projectile launched horizontally from the top of a tall building or a cliff and a projectile that is launched at an angle from the ground. In both types, it should be noted that along the horizontal, there is no force acting and so there is no acceleration in that direction hence motion will stay constant (due to air resistance being ignored), whereas in the vertical direction there is acceleration because of the existence of force of …show more content…
The picture below will present my intended study of projectile motion in the battle. Consider: A castle that is 3,000 metres away To destroy the castle, the cannon would have to hit precisely about the point B from point A. Muzzle velocity of a cannon = 120m/s to 390m/s (but I will use the average velocity to cater for the large indifference) Force of gravity g = 9.81m/s2 Angle (°degrees) Range (m)
X= (V_0^2 sin2θ)/g Maximum height (m) h=(v_0^2 sin〖θ sinθ 〗)/2g Deviation from the range of 3000m
0 0 0 0
30 5740 829 +2740
45 6628 1657 +3628
60 5740 2485 +2740
90 0 3314 -3000
15 3314 222 +314
14 3112 194 +112
13 2906 168 -94
12 2696 143