Mission Possible: Create a Cannon?

imma firing ma cannon...

Yes you heard it...... our physics teacher has snapped..... He is telling us to make weapons of mass destruction..... THE CANNON!!!!
From projectile motion, we learned that the range (x-distance) is:

From this equation, we know that the best angle should be 45 degrees. Why you ask? Well, since we want the maximum distance, every single factor must be maximized. If you calculate the sin of any angle, you will notice that when sin 90, it is equal to 1, its maximum. Therefore is we sub 45 into the equation for range, it will become sin 90, which is the maximum.

Do a barrel roll?

Other factors that will make it better is a longer barrel. Since we are launching a paper cup in class, we want it to be affected by wind resistance for less time. The idea of a longer barrel is that not only will the cup stay in one path for a longer period of time, it will be more protected by the barrel against sideways air resistance therefore it will fly farther forward.