What angle is best when you shoot something to get the farthest distance?

Answer 1

I assume the question is referring to a ball say that is being kicked, in this case some fairly simplistic physics determines that 45 degrees is the perfect angle, this calculation relies upon the fact that the ground is at the same height when it was kicked as when to when it comes to rest. (Delta Yx =0. Hence a level ground)

However... If you are talking about a shot put for instance there is a different story, the optimum angle for this type of throw would be around 42 degrees. This value is different from the first due to the differential in heights between Y(x0) and Y(xfinal) where X is distance, Y states the vertical plane and 0 when t=0 (initial height) and then final when Vx&Vy=0 (aka rest).

A key point to remember in the proof of this is that velocity, time and distance are all independent of mass.

Regardless of how you choose to calculate the initial velocity the explanation stated above is always true for the angle both in a vacuum and in a real world environment. You didn't ask for a scientific proof so in summary:

45 degrees for a ground object (eg. football/soccer)

42 degrees for an object thrown from torso height (eg. shotput) - Approximation