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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 squaredimages 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 curvethat 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: 7,538 Thanks: 920 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: _______ ________ 
January 18th, 2017, 05:34 AM  #3 
Senior Member Joined: May 2016 From: USA Posts: 734 Thanks: 297 
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 
Newbie Joined: Jan 2017 From: Africa Posts: 5 Thanks: 0  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 ? my question was not read or answered properly 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 ?????? 
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: 114 Thanks: 45 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  
Senior Member Joined: May 2016 From: USA Posts: 734 Thanks: 297  Quote:
Quote:
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:
That will look more like a trajectory fired without muzzle elevation from shoulder height on flat ground. The portion of that curve from the yaxis 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:
 
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 
Newbie Joined: Jan 2017 From: Africa Posts: 5 Thanks: 0  parabola
SIMPLE QUESTION Diagram shows trajectory of projectiles  ARE THESE PARABOLAS ? YES OR NO ?  That would solve my problem  Thankyou  ENIGMA 
January 18th, 2017, 01:01 PM  #10 
Senior Member Joined: Sep 2015 From: CA Posts: 1,289 Thanks: 664  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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definition, difference, hyperbola, parabola, simple 
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