Talk:Range of a projectile

"maximum distance of the range of a projectile"
What does this even mean? Why are the variables in the formula not defined? What is "Projectile Physics Sydney" (Google knows nothing) and why is it not referenced? I suggest this part of the article be removed. --Msittig (talk) 04:41, 19 November 2014 (UTC) Reference "maximum distance of the range of a projectile” The formula for angle for max range is incorrect When I used v=146.67 ft/sec, yo=100 feet and g=32.174 ft/sec sq, your formula gives 55.6 degrees and I get 41.3 by iteration though angles of theta I also solved for the Sin(Theta) that macked the derivative of distance =0 and also got theta=41.3 degrees

Effect of variables on range?
Would it be worth including a section on how changing each of the variables would affect the range? I was looking for something like this and, while the initial equation was helpful, the rest was not as useful.--86.17.211.228 11:54, 2 December 2007 (UTC)

Forward shot
If shot at ground level in flat ground, directly ahead, θ would be 0... But this would result in the operatino giving 0 as the length of the range, how does oen calculates such a shot? Besides... There is no data whether speed to be used has to be in m/s, km/s or km/hr...Undead Herle King (talk) 04:39, 22 September 2008 (UTC)


 * Yes, the range really is zero. If the projectile is shot at ground level on flat ground, then it hits the ground immediately. It may well continue moving, but it's much farther from ideal projectile motion (due to friction and support against gravity) than when the projectile is in the air. And it doesn't matter what units you use — as long as they're consistent, it'll work. Consistent means that for some length unit a and time unit b, your initial speed must be given in a / b units, your value for g in a / b 2 units, and the result will be in a units. --216.171.188.181 (talk) 20:48, 12 February 2009 (UTC)

The math is great, but a lot is missing
Really, this is all about ideal projectile motion, rather than actual projectile motion, where things like air resistance have to be accounted for. I'm going to tinker with it a bit, but someone who knows about the effects of projectile size, shape, and mass; and barrel length and rifling, for instance, could add a lot. --Badger151 (talk) 14:42, 27 February 2010 (UTC)
 * Well, that's about as far as I can take it. I've added sections discussing air resistance, the characteristics of the projectile, and the characteristics of a launching firearm's barrel, but I can't begin to tackle the math. --Badger151 (talk) 16:26, 27 February 2010 (UTC)

maximal range
--Guerinsylvie (talk) 10:35, 26 July 2010 (UTC) :- Good morning ; i am french-locutor ; so, please, excuse my bad english.

angle between (Oz, OP) = $$\phi $$, distance OP = r, with :
 * The maximal range is given by the equation of the parabola of safety.
 * This work was made by Torricelli in 1641.
 * In modern notation, let be $$ \alpha = \pi/2 - \theta$$ : Torricelli has demonstrated that the point of contact between the trajectory and the parabola-of-safety is given by his polar coordinates :


 * $$\phi = 2 \cdot \alpha $$
 * $$r = \frac{h}{cos^2 \alpha} $$, with $$ h = \frac{V_0^2}{2g} $$, therefore $$r = \frac{2h}{1+cos \phi} $$

{Of course, his demonstration was geometric ( Descartes's geometry is not still available ). But it is easy to show analytically ( I can show, if you want ; and of course, you need not any derivative : before Leibniz, no derivative !).}

This very-simple equation makes this : "it is not surprisingly simple expression", it is simplely because there is a prettier manner of demonstration : the original one, the Torricelli's one. In fact, the formula :
 * $$ \theta = \arccos \sqrt { \frac {2 g y_0 + v^2} {2 g y_0 + 2 v^2} }$$

is written as :


 * $$cos 2\theta = sin 2\alpha = \frac{y_0}{r}= \frac{y_0}{2h+y_0} $$, with $$ h = \frac{V_0^2}{2g} $$ ,

and, better : $$\pi/2 - \theta =\alpha = \phi/2 ~$$.

It seems to me easyer to memorize : shoot at the bissectrice, said Torricelli !{of course, you need draw the picture, to obtain the intersection}

So, the résult is immediatly : OP = 240 m and y= 40m ; therefore cos ( 2\theta) = 40/240 = 1/6 ,therefore ~ \Pi/2 -1/12. Of course the horizontal-range is near 240m.
 * For the example, I suggest the following, more easy ( but I choose similar data, of course ) : h = 100m and y= 40m.
 * For my pupils, I preferred this example : the weight range :

a man ( yo = 1.80 m) throw out a weight ( Vo such as h = 10m) : guess the optimal angle : the pupils answer : ~ ( \pi/2 - yo /4h). And no need more precision, because air resistance. {remark : of course, if yo << h, the answer is trivial : \alpha ~ yo/4h ! }

¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤

All this results are well known ; none are mine.

best respects. guerinsylvie.

to perform the demonstration of "maximal range"
--Guerinsylvie (talk) 10:58, 8 August 2010 (UTC) :- before the destruction, I had to perform the demonstratio ; you can look at it, on my page of discussion ( I am new, on this english-WP, and I don't want perturb)

Maximum range ignores speed and gravity
in the equation, speed should not matter as it is a constant not a variable, the ratio should always be the same no matter speed, therefore the same should also go for gravity (as gravity is just a multiplier of speed if you fundamentally break it down) so the only 2 variables the equation should include are initial height and angle —Preceding unsigned comment added by 204.10.219.142 (talk) 16:14, 6 October 2010 (UTC)

I think the basic equation in this article has an error. The equation reads


 * $$ d = \frac{v \cos \theta}{g} \left( v \sin \theta + \sqrt{v^2 \sin^2 \theta + 2gy_0} \right) $$

but I think it should be


 * $$ d = \frac{v \cos \theta}{g} \left( v \sin \theta + \sqrt{v^2 \sin^2 \theta - 2gy_0} \right) $$,

that is, the + sign before the 2gy0 term should be a minus sign. Clearly the equation is wrong; since every term is positive, it implies that as y0 goes to infinity, so does d. But this doesn't make physical sense for a fixed v and theta, for which the range is finite even when y0 = 0. — Preceding unsigned comment added by Amtravco (talk • contribs) 02:53, 27 January 2017 (UTC)

Definition missing
Hi Wikipedians, the intro paragraph does not clearly define what is "range", to whoever doesn't want to go thru detailed maths. Can anyone please help summarizing the concept in plain words? Thanks, DPdH (talk) 23:12, 1 April 2018 (UTC)

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