Weaponry

There are several iconic weapons that the swashbuckling pirates have in their armory: cannons, muzzle-loaders, sabres. But for our purposes we will discuss both muzzle-loaders and cannons.

Physics of Projectiles:

Considering the cannon ball and bullet as a projectile, at first negating the need for black powder as a propellant, the projectiles follow the classical Newtonian physics.
To simplify this situation one could turn a cannon ball and/or bullet flying into a 2-D kinematic equation.

Projectile Motion

image made in paint by me but copied from image 4.14 on page 92 from Knight

After the projectiles are launched from the barrel of either the gun or cannon, they are shot at an angle called their 'launch angle'.
Projectiles have a trajectory of a parabolic shape due to the fact that after it's initial launch the object is essentially in free fall, according to Knight. (Knight, 92).

Kinematic Equations:

Terms:

            v(0,y)=v(0)sin(theta)
            v(0,x)=v(0)cos(theta)
            a(x)=0
            a(y)=-g          {acceleration terms are this due to projectiles in free fall}

1) x(f)=x(i)+v(i,x)*(delta t)

2)v(f,x)=v(i,x)=C

3)y(f)=y(i)+v(i,y)*(delta t)-.5*g*
(delta t)^2
4)v(f,y)=v(i,y)-g*(delta t)
equations found in Knight pg 94

Although this is a quite simplified for the purpose of a real world problem, one can get quite close to what the actual answer is by adding in the additional conditions like the wind velocity and the spin of the projectile for example.

Physics of a Pirates' Life

Weapons:

Physics of Projectiles:

Projectile Motion

Kinematic Equations: