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?
2007-06-30
13:44:31
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3 answers
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asked by
smci
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Sports
➔ Outdoor Recreation
➔ Hunting
(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
2007-06-30
17:06:44 ·
update #1