What is the best angle for maximum distance?

Question

I am building an air cannon for my science fair project. The question is "What is the best possible angle for the most distance when firing a projectile?". I thought it might be 45 degrees (because 45 degrees is the perfect balance between straight up and straight forward) but I have been told it isn't 45 degrees. I thought about it and i have come to the conclusion that it must be a lower angle because of gravity and air resistance. I would also like any websites addressing this topic.

Answer 1

Ignoring air-resistance, the horizintal distance covered by an object projected with a velocity, v, and at an angle of θ from the horizontals is:

s = v²sin(2θ)/g

Assuming constant velocity and gravitational force, s is maximised when sin(2θ) is maximised. sin(2θ) cannot be greater than 1. sin(2θ)=1 when θ = 45°.

Answer 2

It's 45 deg.
The motion of an object under the influence of gravity is determined completely by the acceleration of gravity, its launch speed, and launch angle provided air friction is negligible. The horizontal and vertical motions may be separated and described by the general motion equations for constant acceleration. The initial vector components of the velocity are used in the equations. The diagram shows trajectories with the same launch speed but different launch angles. Note that the 60 and 30 degree trajectories have the same range, as do any pair of launches at complementary angles. The launch at 45 degrees gives the maximum range.

Answer 3

45 is the optimum angle. The air resistance is negligible.
d=xo+vot+1/2at^2

Answer 4

every 1 says 45, but i think its 46. to complicated to explain.