My Math Forum Difference between parabola & hyperbola --simple definition

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 January 18th, 2017, 02:13 AM #1 Newbie   Joined: Jan 2017 From: Africa Posts: 5 Thanks: 0 Difference between parabola & hyperbola --simple definition Hi --- As a complete math idiot ( failed high school math twice ) but achieved above average results in all other subjects -- Persistent problem ---a rifle trajectory ---is shown as a parabola --PARABOLA ? I d/loaded a parabola --- X= Y squared-----images ---etc quite simple ---a steep side U SHAPED CURVE appeared!! A parabola -- --to my riflesmith /hunter /archer 67 yr old mind is a ARC or gentle curve---that is a bullet or cannon ball ---affected by gravity so the gentle curve --becomes a sudden down turn into the earth --BANG ! Why does a PHD math professor whom I asked to clarify this anomaly / tell me PARABOLA can be inverted ---still a parabola -- and a cannon ball or bullet or missile ---describes a aPARABOLIC curve !!! to me -this is total nonsense --common sense 50 yrs of hunting shows a bullet Cannot fly down --then up in a U shaped curve --as in X= Y sq graph !! I= PROJECTILES do not fly in a neat curve -as shown in the graph -- can anyone sort out this confusion -- ( When--- the math professor got fed up with my argument -- he pompously began using the mystery term "" FUNCTION!! t=That was the end for me --had no idea what he was on about as I could not really grasp the PARABOLA /HYPRBOLA graph idea as a bullet trajectory --could someone give me a VERY FUNDAMENTAL SIMPLIFIED ANSWER to my problem ---kindly leave out all fancy jargon please!~! simple basic solution is all I ask for --this problem has been ongoing for over 40 yrs ----never had a clear explanation !! appreciate / WILL be eternally grateful --to anyone who dares to answer this problem ---in a simple concise way ---(remember --my math abilities are not great) regards --- ENIGMA Yet
 January 18th, 2017, 04:52 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,595 Thanks: 938 Math Focus: Elementary mathematics and beyond When the bullet leaves the muzzle it travels a straight line. When sufficient speed is lost the bullet starts to drop to the ground. We're looking at something like Code: ----------------------------------_______ ----------________ Maybe half of a parabola, from where the bullet starts to drop.
 January 18th, 2017, 05:34 AM #3 Senior Member   Joined: May 2016 From: USA Posts: 803 Thanks: 319 First, a bullet's trajectory being a parabola is an idealization, meaning that it will be true if the bullet is affected after leaving the muzzle ONLY by gravity. In actuality of course, the trajectory of the bullet is also affected by wind resistance and by the fact that the surface of the earth is not flat. So in the real world, the parabola is just an approximation of the trajectory. It is a very good approximation, but not an exact description (unless you are shooting on the moon). Second, a parabola is not a single curve. It is the name of an infinite number of curves, each of infinite length. It is much more exact to say that a bullet's trajectory is, to a very close approximation, described by a very small part of a parabola. Third, the kind of parabola depends on the muzzle velocity and the angle (the "elevation") between the ground and the barrel of the rifle. The kind of parabola if the barrel is parallel with the ground is half of an upside down U, considering only the falling part of the curve. The U shape you are thinking about is not meant at all. Moreover, it is very flat, meaning that it is not very different from a straight line. To get a trajectory described by a more typical but still upside down parabola requires shooting with elevation, in which case the bullet does move upward initially before beginning to fall. If you shoot at a flying bird, you aim upwards, but the bullet eventually falls to earth so the trajectory clearly is not a straight line when you aim upwards. Finally, to explain why the IDEALIZED trajectory is PART of an upside down parabola that is strongly curved only if there is significant elevation takes a lot of math, but it should be clear that bullets do not move in straight lines. When firing at a distant target at ground level, you do not aim directly at the target, but somewhat above it, because experience proves to you that BULLETS DO NOT TRAVEL IN PERFECTLY STRAIGHT LINES.
January 18th, 2017, 05:42 AM   #4
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maybe half a parabola??

I must be hallucinating ?
a bullet trajectory ---is represented by a series of steps /straight lines?
no curve ---when gravity takes over ?

ie how can a V or U shape ---be a PARABOLA ( SEE GRAPH I attached !)

IS THIS A PARABOLA ??? or some sick joke ?

can a bullet or cannon ball ---describe such a ridiculous trajectory??

X= Y squared ?---
a bullet -one expert declared described a parabolic ARC
--- THEN showed this graph of X= Y sq

----can anyone believe this ??????
Attached Images
 GRAPH SHOWS X= Y SQUARED ---a V or U shape ----.jpg (13.0 KB, 2 views)

 January 18th, 2017, 05:55 AM #5 Newbie   Joined: Jan 2017 From: Africa Posts: 5 Thanks: 0 Any child knows a pea shooter or slingshot ---does not have a FLAT trajectory hunting for 50 yrs ----- The MRT of 30 .06 SPORTING rifle ---ie max elevation b4 gravity pulls the 180 grain bullet earthwards is around 170 -190 yards ---depending on sea level -- a gentle curve at first --followed by a increased curve DOWNWARDS ---is what I expect --and proved Yet I am told /shown a graph --- of X= y sq ---and that is called a Parabola ?????---a V shape ?? so what IS A HYPERBOLA ??? My question -- is ---why is a bullet trajectory --named X= Y sq --- then a ridiculous shape graph is presented !!! mind boggles ----
 January 18th, 2017, 06:12 AM #6 Senior Member   Joined: Sep 2016 From: USA Posts: 167 Thanks: 78 Math Focus: Dynamical systems, analytic function theory, numerics Turn your parabola upside down. Then stretch it out so it is wider. Now it looks like a bullet trajectory. Also, it is still a parabola.
January 18th, 2017, 06:48 AM   #7
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Quote:
 Originally Posted by ENIGMA Any child knows a pea shooter or slingshot ---does not have a FLAT trajectory
So if it is not flat, it must be a curve. The only question is what kind of curve it is mathematically.

Quote:
 hunting for 50 yrs ----- The MRT of 30 .06 SPORTING rifle ---ie max elevation b4 gravity pulls the 180 grain bullet earthwards is around 170 -190 yards ---depending on sea level -- a gentle curve at first --followed by a increased curve DOWNWARDS ---is what I expect --and proved
And those are the characteristic attributes of part of one kind of a parabola. If you had the courtesy and sense to read carefully what was written, you would have seen that I said that the parabolas relevant to trajectories are rotated relative to the U shape that you keep saying is THE parabola and that only part of the relevant parabola is involved. Parabolas come in many different shapes and orientations: some woman are blondes, but that does not make all women blondes.

So you have proved that all trajectories are downward. Amazing: I wonder then how people shoot birds on the wing. All trajectories on earth of slow enough objects EVENTUALLY go downward, but the INITIAL trajectory may be upward. Think about upside down parabolas as was previously suggested and rotated parabolas.

Quote:
 Yet I am told /shown a graph --- of X= y sq ---and that is called a Parabola ?????---a V shape ?? so what IS A HYPERBOLA ???
Try graphing $y = 5.5 - 0.1x^2.$

That will look more like a trajectory fired without muzzle elevation from shoulder height on flat ground.

The portion of that curve from the y-axis to the x=axis is just as much a parabola as the one you graphed. Not a hyperbola. Hyperbolas have nothing to do with trajectories.

Quote:
 My question -- is ---why is a bullet trajectory --named X= Y sq --- then a ridiculous shape graph is presented !!! mind boggles ----
The mind boggles that you imagine anyone ever meant that. You did not bother to read what was a fairly detailed explanation that should have made quite clear that what you imagined was the only possible parabola is not the only possible parabola and that what people are talking about when saying that trajectories are approximately parabolic are parabolas flatter than, and either rotated or inverted relative to, the parabola that you have graphed. You do not bother to try to understand the explanations that you asked for, but prefer to glory in your ignorance.

 January 18th, 2017, 09:20 AM #8 Newbie   Joined: Jan 2017 From: Africa Posts: 5 Thanks: 0 Thanks JEFF -- Instead of ranting at me for my poor math --- rather --prove your assertions --by supplying me with clear concise DIAGRAMS to illustrate what you keep going on about ---I am now totally lost with all your diabolical and cynical assertions -- a simple cannonball fired in a arc --has now become a complicated set of frightening geometrical formulas ------ ? that includes all factors affecting its flight path --wind /gravity etc Prove that the V SHAPE is not a true parabola -but some distorted geometrical nightmare that simply fits the equation nicely ---ie Y= X sq --- A parabola -- can you draw or sketch a simple cannon balls trajectory - showing all the obviously complex math formulas --along its curve ? and then maybe I will grasp the idea of a flattened --opened up parabola -- but that V shape called a parabola ? you still have not explained clearly --WHY is called a parabola !! Then I am told its not a true version of bullet trajectory --the sharp V --must be pulled open ???? to create a gentle curve ?? so why did the professor not clarify this obvious point --when I disagreed on the SHAPE OF THAT V ??? If this question is too vexing or annoying ---feel free to abort -I will try another forum --for a clarification --without the headmasters stern rebuke- and dark sarcasm --- no wonder there are millions who drop out of this nightmare ---too many patronising experts --who refuse to take the time to illustrate a long verbal diatribe !! ok --see ya == no point in continuing this nonsensical argument without clear illustrations --
January 18th, 2017, 10:56 AM   #9
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parabola

SIMPLE QUESTION

---Diagram shows trajectory of projectiles ---

---ARE THESE PARABOLAS ? YES OR NO ?
--- That would solve my problem --

Thankyou --
ENIGMA
Attached Images
 TRAJECTORY OF BULLET OR CANNONBALL_ballistic_trajectories_velocities_svg.jpg (13.9 KB, 1 views)

January 18th, 2017, 01:01 PM   #10
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Quote:
 Originally Posted by ENIGMA SIMPLE QUESTION ---Diagram shows trajectory of projectiles --- ---ARE THESE PARABOLAS ? YES OR NO ? --- That would solve my problem -- Thankyou -- ENIGMA
what you've drawn look like ballistic trajectories that include air resistance, so they aren't exactly parabolas, but yes they are approximately parabolas.

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