|January 18th, 2017, 03:13 AM||#1|
Joined: Jan 2017
Difference between parabola & hyperbola --simple definition
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)
|January 18th, 2017, 05:52 AM||#2|
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City
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
|January 18th, 2017, 06:34 AM||#3|
Joined: May 2016
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, 06:42 AM||#4|
Joined: Jan 2017
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, 06:55 AM||#5|
Joined: Jan 2017
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, 07:12 AM||#6|
Joined: Sep 2016
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, 07:48 AM||#7|
Joined: May 2016
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.
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.
|January 18th, 2017, 10:20 AM||#8|
Joined: Jan 2017
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, 11:56 AM||#9|
Joined: Jan 2017
---Diagram shows trajectory of projectiles ---
---ARE THESE PARABOLAS ? YES OR NO ?
--- That would solve my problem --
|January 18th, 2017, 02:01 PM||#10|
Joined: Sep 2015
|definition, difference, hyperbola, parabola, simple|
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