CANNONS!

One of the most recognizable structures in human history, the cannon is considered by some to be the pinnacle of warfare artillery. However, behind its thick shell and stern reputation lies an engineering marvel. It might seem strange, but physics is the backbone of the cannon.

A complicated cannon; assembled in a manner so that it remains hidden behind a barricade

As a project, our class will be building cannons on Thursday. The materials are a maximum of 5 soda cans, duct tape, and two Styrofoam cups. First of all, I believe that the cannon will be more successful if we make sure the inner part of the cannon is very smooth. This reduces the amount of friction that the cannon ball will experience. Also, the cannon barrel should be quite long, instead of very short. This way, the cannon ball will not experience as much air resistance when it leaves the cannon. Regarding the cannon ball itself, it might not actually have to be a ball. Looking at fast airplanes and cars, it seems that the most prevalent form of aerodynamic structure is a pointed tip. For example, F15 fighter jets are designed so that they are highly aerodynamic. The reason that these airplanes are so aerodynamic is because of their shape. When moving through the air, air resistance will be evenly distributed along the airplane rather than hitting it with a very strong force. (Newton's third law: every action has an opposite and equal reaction).

F15 Silent Eagle fighter jet

Now, for the angle of the cannon. In the kinematics unit, we learned about projectile motion. We learned the equation:

In this equation, d is the horizontal distance traveled, v is the velocity of the projectile and g is the force of gravity. From looking at this equation, we can already determine that the largest angle at which the cannon can be fired is 90°. This is because anything greater than that will result in a cannon that shoots straight upward or backwards (in other words a cannon that is not fit for combat). Thus, the angle must be less than 90°. But what angle will allow us to maximize the distance traveled? This is where the equation comes into place. 

Isolate sin2theta.

Using this equation, another clue is found. It appears that if theta = 45°, then the d will be be maximized. 
Since sin (45x2) = sin 90=1, therefore 45° will likely produce the farthest distance traveled.

This is because if theta=45°, then 2xtheta would equal 90°.