For as long as humankind has existed, humans have engaged in war. In the early ages, swords were used, but as technology improved, so did the weapons. And with the invention of gunpowder, came the invention of the cannon. The first cannon was documented in the 12th century in China, and quickly became very important in the many wars during the middle ages. The cannon fires a projectile, and understanding and modelling its motion has been imperative to use it correctly. This maths exploration will explore the projectile motion of the objects projected from a cannon.
Modelling projectile motion is crucial in understanding the motion of the projectile, and a simple cartesian coordinate system can be used, in which the motion starts at the origin:…show more content… In order to get a proper expression, two factors need to be included: gravitational acceleration and the air resistance of the projectile. The gravitational acceleration only works on the vertical component, hence has no impact on the horizontal velocity. To further examine the motion and forces of the projectile, the mass must be considered, given by m.
So, first considering the gravitational acceleration (g), ax=0 and ay=-g
The acceleration due to air resistance is a little more complex, and first we must find an expression for the force due to air resistance. Supposing that the force due to air resistance is directly proportional to the velocity of the projectile relative to air: fair=rV Where r is the air resistance constant. Since the direction of the air resistance is opposite to the velocity of the projectile, resolving the vector gives:
fairx=-rVx fairy=-rVy Given Newton’s second law of motion, F=ma, we get:
