DIY Solar Panels

For projectiles, 45° is only necessarily the optimal launch angle if ALL of the following apply – otherwise you have to consider specific cases of the eqns:

- the elevation of launch and landing are both equal => s_y(0) = s_y(t1) (usually taken as reference 0, but it’s irrelevant)

- there are no obstacles to be cleared along the trajectory
(i.e. elevation of the terrain s_y(x) <= 0)

- there is no (or negligible) wind or resistance force (e.g. air resistance) => a_x = 0, a_y = -mg

- there is both correct rifling and the bullet is balanced, so that the projectile does not exhibit precession and yaw off at unreliable angles. (http://en.wikipedia.org/wiki/Rifling)
For a gun, the bullet fits the barrel, the grooves are correctly machined to match it, and the exhaust gases are symmetric (may depend on venting).

- For a weapon, the shooter did not move while shooting.
Not sure if the terrain affects whether recoil forces work.

How many more valid reasons can you suggest?
(Sorry for not clarifying ‘optimal’, the browser has been crashing on me for last 2 hrs.)

45° is only the optimal launch angle to maximize range at the expense of everything else (e.g. accuracy, impact velocity i.e. deadliness).
Obvously if you shoot a gun at 45° you will have little accuracy and the bullet will definitely precess.

I should have said there are (at least) two modes of launching a projectile:

- short-range, where we maximize accuracy and impact speed e.g. guns, rifles

- ballistic: long-range artillery, trebuchets

45 may not be a correct launch angle depending on terrain. if your using a short range round like a mortar you may want to use even more elevation to get over hills, building trees and have the projectile straight down. To be honest its something inever really considered