# Naked Science Forum

## Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Yahya on 07/01/2017 17:58:04

Title: How long does a stone thrown into the air spend stationary at the highest point?
Post by: Yahya on 07/01/2017 17:58:04
when I throw a stone upward exactly vertical ( 90 degrees angle )with a particular initial speed, what is the duration at which its velocity is exactly zero? suppose it stops at a particular height, how long it will take while it is at this height ?
Title: Re: how long a stone will take while its velocity is zero?
Post by: yor_on on 07/01/2017 21:49:34
de4pends on gravity. atmosphere, mass, speed, etc. You want to specify it? Maybe the idea is one of there being a 'equivalence' adapting those factors?
Title: Re: how long a stone will take while its velocity is zero?
Post by: zx16 on 08/01/2017 00:31:33
when I throw a stone upward exactly vertical ( 90 degrees angle )with a particular initial speed, what is the duration at which its velocity is exactly zero? suppose it stops at a particular height, how long it will take while it is at this height ?

Your question is deep.  It depends on whether the flow of time is smooth and indivisible.  Or whether time is made of discrete particles such as "chronotrons"

If time is made of chronotrons,  then your up-thrown stone would stay still -  at zero-velocity -  for precisely 1 chronotron.  Then it would reverse direction, and fall back down again.

Title: Re: how long a stone will take while its velocity is zero?
Post by: chiralSPO on 08/01/2017 03:09:47
Trying to answer this very precisely would require more precise definitions. For instance, all of the atoms within the stone are moving randomly at incredibly high frequencies, so are we talking about the center of gravity of the stone, or the average velocity of all of the constituents of the stone? Also, whose perspective are we using as the frame of reference for determining the velocity of the stone?

I think it would be very hard to specify an amount of time that the stone actually had zero velocity. We could calculate some incredibly short window of time for which the momentum of the stone would be within the Heisenberg Uncertainty limit of zero given what is known about the location of the stone....
Title: Re: how long a stone will take while its velocity is zero?
Post by: Yahya on 08/01/2017 07:28:23
I think the answer is : it spend at that point zero time , it spends nothing , a moving particle spend nothing when it is at a particular point apart from its velocity  , when we want to measure the time elapsed for this point , we set the time to be zero at the start point, because in fact the time is zero.

Title: Re: how long a stone will take while its velocity is zero?
Post by: evan_au on 08/01/2017 09:04:19
Quote
I think the answer is : it spend at that point zero time
- The acceleration of the stone is (almost) constant.
- the velocity starts off negative (upwards) and increases in an (almost) straight line until it reaches the same value, but positive (downwards)
- the amount of time spent crossing the v=0 axis is 0 seconds
- this answer doesn't really change if you add in the inverse square law of gravity, or air resistance
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: chris on 08/01/2017 09:26:03
This is a really nice question that highlights a common misconception. Many people, especially younger learners, get the idea that a ball or stone launched skywards "pauses" for a while at the top of its travel before it falls again.

Actually that pause is only instantaneous. The object is constantly slowing down as gravity accelerates it downwards. At some point the velocity is transiently zero before it begins to accelerate groundwards again.

The reason the object appears to pause is that as it approaches standstill it is moving progressively more slowly. As it begins to accelerate down again it is also initially travelling only very slowly.

The net result is that it looks like it's stopped in mid air for a bit.
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: Yahya on 09/01/2017 08:43:44
"everything should be as simple as it can be, but not simpler" Albert Einstein
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: zx16 on 09/01/2017 21:39:52
This is a really nice question that highlights a common misconception. Many people, especially younger learners, get the idea that a ball or stone launched skywards "pauses" for a while at the top of its travel before it falls again.

Actually that pause is only instantaneous. The object is constantly slowing down as gravity accelerates it downwards. At some point the velocity is transiently zero before it begins to accelerate groundwards again.

The reason the object appears to pause is that as it approaches standstill it is moving progressively more slowly. As it begins to accelerate down again it is also initially travelling only very slowly.

The net result is that it looks like it's stopped in mid air for a bit.

Surely the object doesn't just "look like it's stopped".  It must actually have stopped going upwards, before it can start going downwards.

I mean the object can't be moving in two directions - upwards and downwards - at the same time. Surely there must be a "instant" in time at which the upward movement stops?  Before the downward movement can start.

And mightn't this "instant" be defined, in the particle-based physics which is absolutely required at present -  as 1 chronotron.
Couldn't the chronotron  explain Time, just like the Higg's Boson explains Mass. The Higg's Boson was (supposedly) detected  by the LHC.

Would it possible for us to build a"Chronotron" detector?
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: chiralSPO on 09/01/2017 22:43:02
Surely the object doesn't just "look like it's stopped".  It must actually have stopped going upwards, before it can start going downwards.

The standard explanation is that it has stopped instantaneously before reversing directions. But I believe what chris was referring to is the illusion that an object hangs for a finite moment before reversing course. For instance, if one counts g as 9.8 m/s2, an object would spend about 200 microseconds (a far cry from instantaneous) with a speed less than 1 mm/s (a far cry from 0, but maybe not distinguishable by a casual observer)

I mean the object can't be moving in two directions - upwards and downwards - at the same time. Surely there must be a "instant" in time at which the upward movement stops?  Before the downward movement can start.

This depends on your definitions of "moving," "object," and "same time." :-)
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: zx16 on 09/01/2017 23:12:23
It's Zeno's arrow all over again - after 2,000 years!
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: nilak on 09/01/2017 23:23:05
The object will stay exactly as newtonian mechanics would predict- an infinitesimal amount of time.
In newtonian mechanics you can throw an object perfectly vertical and then at some point it stops and stays there for  an infinitesimal amount of time.
If I interpret this using my theory, there is no such a thing as an object at rest. This also violates time asymmetry. However you can theoretical assign a centre to a structure with a certain degree of precision (you can't have perfect precision not even theoretically, sounds a bit like the uncertainty principle but this is something else) and that center will at some point stop and stay for an instant like in newtonian mechanics.
The best way to answer  your question in the real context is by the motion or a beam of light in a gravitational field. If you imagine sending a beam of light at 1 degree instead of 90deg, it will reach a certain height then it will go down following a parabolic trajectory . You can see that it never actually stop,
but it will stay at the top for an instant of time.
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: Yahya on 10/01/2017 05:52:05
time being infinitely small violates velocity definition , if there is distance elapsed then there is time taken and vice versa, if there is not any distance elapsed( supposing this is the definition of this stone at zero velocity because if it take any tiny distance downward its velocity will start to increase ) then there is not any time taken, this for any object moving, if its distance is zero and it takes time then its instantaneous velocity is 0/t =0 , for a moving object its instantaneous velocity can not be zero.
we can apply this rule for this stone because when its velocity is zero , that mean it is in an exact point, think of a number line , to the right are positive numbers and to the left are negative numbers, where is the zero ? it is at the exact point between the two.
you can think of the stone as a particle moving through the number line from the right to the left.
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: nilak on 10/01/2017 08:43:31
v=dx/dt    But dx and dt are not 0.
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: Yahya on 10/01/2017 09:08:03
they are. 0/0 can equal any number according to the situation , according to the smallest number the denominator  and numerator were  before they became zero, if the ratio equals a specific number, and the nominator decrease and the denominator decreases as well but keeping the same ratio , then they will end up in 0/0 but still the ratio the same  in this case 0/0 equals the instantaneous velocity (instantaneous velocity is constant) , remember also that : 0/0=any number, because 0=0*anynumber. and in the real world they are.
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: nilak on 10/01/2017 09:52:57
You can never divide by pure zero.
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: Yahya on 10/01/2017 10:16:30
You can never divide by pure zero.
it's just my personal explanation.
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: nilak on 10/01/2017 10:45:21
You need to learn calculus to understand the mathematical concepts. However we don't know how infinity and infinitesimal quantities occur in reality.
An example of an infinitesimal number can be 1-0.(9)    0.(9)is 0.999... basically you add an infinite amount of 9 decimals.

For the speed of light c=3*10^8 m/s = x/t=dx/dt
x=3*10^8
t=1
dx=x/n=3*10^8/n
dt=t/n=1/n
where n is a very large number.
Even if n tends to infinity dx/dt remains the same 3*10^8m/s

If we take a number r0=1 we can't really say what is the next real number because there is no next number.
If n tends to infinity then the next number after r can be thought as r1=r0+1/n then r2=r0+1/n+1/n=r0+2/n
All of these are only mathematical solutions.
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: evan_au on 10/01/2017 11:19:07
v=dx/dt    But dx and dt are not 0.
In calculus, v is normally expressed as "the limit as dt approaches 0. "

For a well-behaved function (like an object lobbed in a gravitational field), v is well-behaved as dt approaches 0, and when dt = 0. See L'Hopital's rule.
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: nilak on 10/01/2017 11:38:14
v=dx/dt    But dx and dt are not 0.
... and when dt = 0. See L'Hopital's rule.
dt can never be pure zero. That is the purpose of "d"
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: Yahya on 10/01/2017 12:02:49
dt can never be pure zero. That is the purpose of "d"
an object at stationary , it elapses zero distance and the time it takes zero at an instant ( because when start to count time will first be zero ) how do you determine its velocity , there is not limits here , zero distance and zero time ? similar problem for the stone. but we all know this velocity is zero , and the stone velocity has the instantaneous velocity , how 0/0=0 ? 0/0=anynumber
but fortunately we know its velocity is zero , because it will still not make displacement and then v=0/t=0 , for the stone its velocity is the instantaneous velocity taken from the slope of the graph.
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: jeffreyH on 10/01/2017 18:23:52
v dt = dx.
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: chris on 12/01/2017 08:37:00
In calculus, v is normally expressed as "the limit as dt approaches 0. "
For a well-behaved function (like an object lobbed in a gravitational field), v is well-behaved as dt approaches 0, and when dt = 0. See L'Hopital's rule.

Who was L'Hopital?
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: jeffreyH on 12/01/2017 18:49:51
In calculus, v is normally expressed as "the limit as dt approaches 0. "
For a well-behaved function (like an object lobbed in a gravitational field), v is well-behaved as dt approaches 0, and when dt = 0. See L'Hopital's rule.

Who was L'Hopital?

https://en.m.wikipedia.org/wiki/Guillaume_de_l'H%C3%B4pital (https://en.m.wikipedia.org/wiki/Guillaume_de_l'H%C3%B4pital)
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: Yahya on 13/01/2017 07:25:58
The object will stay exactly as newtonian mechanics would predict- an infinitesimal amount of time.
does that mean that I'm the only one who has this idea?
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: Yahya on 13/01/2017 07:29:02
You need to learn calculus to understand the mathematical concepts.
I learned calculus....
v=dx/dt    But dx and dt are not 0.
but I learned that if dx/dt=0/0 that does not mean an answer does not exist.
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: evan_au on 13/01/2017 10:16:06
'It depends on whether the flow of time is smooth and indivisible.  Or whether time is made of discrete particles such as "chronotrons" '
If time is quantized, it hasn't shown up at the very small timescale  events probed by the high energies in the LHC.

A Stone has much lower energy per nucleon than particles in the LHC, so we can effectively treat time as continuous.

It is possible that time is quantised on very small timescales; and it may even have macroscopic side-effects. Just as quantised energy levels in atoms avoided the immediate collapse of all atoms in the universe, it is possible that quantised time may someday explain some other phenomenon like persistent infinities around black holes.

But for stones falling in Earth's gravity, treat time as continuous.
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: nilak on 13/01/2017 11:44:11
The object will stay exactly as newtonian mechanics would predict- an infinitesimal amount of time.
does that mean that I'm the only one who has this idea?

The object really stops at the top and v reaches absolute zero according to newtonian mechanics. However according to my concept this never happens because my concept uses waves propagation to explain motion and all propagations are at a constant speed c and obviously never stop.
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: Colin2B on 23/11/2017 12:29:51
does that mean that I'm the only one who has this idea?
No. Newton and his peers knew about this which is one of the reasons they were interested in the development of calculus.
I think the answer is : it spend at that point zero time
- The acceleration of the stone is (almost) constant.
- the velocity starts off negative (upwards) and increases in an (almost) straight line until it reaches the same value, but positive (downwards)
- the amount of time spent crossing the v=0 axis is 0 seconds
- this answer doesn't really change if you add in the inverse square law of gravity, or air resistance
but the confusion can be better explained if you avoid talking about an object only having a vertical component of velocity.
Consider an object thrown with both vertical and horizontal velocity components. The object will reach the apex and have zero velocity at a specific time - the turnaround point. That time is a specific point on the curve and if you zoom in to that point it gets smaller and smaller trending towards 0 in both velocity and time. So the problem is not another Zeno paradox as suggested earlier, but a fractal effect.
If we look at the way Newtonian mechanics calculates the total time the object is in flight we find it is symmetric around the apex ie no time is allowed for any hold or hesitation at the apex - this you will find on many school homework sites.
As @evan_au says, it can only be considered to spend any time at the apex if time is quantised and as yet we have no evidence for that.

Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: jeffreyH on 23/11/2017 13:09:06
According to quantum mechanics neither space nor time are quantized. Only energy has quanta. From the continuums of space and time the magnitude of the energy quanta can be derived
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: geordief on 23/11/2017 14:13:12
Is the object not just following its trajectory in curved spacetime ?
What would its trajectory look  like  if it was modeled    in this way?

Would it not be similar to an object moving on the surface of the Earth with the difference that the latter is being constantly accelerated out from the centre of the Earth whereas the stone is in freefall immediately following its initial upward acceleration?

I wonder whether this "infinitesimal pause"  might be modeled as  simply a point on a geodesic in the curved spacetime model and the question not arise.
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: Colin2B on 23/11/2017 14:25:28
I wonder whether this "infinitesimal pause"  might be modeled as  simply a point on a geodesic in the curved spacetime model and the question not arise.
Firstly, it isn’t an infinitesimal pause it is genuinely a dt=0 at v=0. It is only infinitesimal if you choose to zoom out and sacrifice accuracy.
Yes, it can be modelled as a point on the geodesic, but that is exactly the same as modelling the point on the apex of the trajectory curve as described above, just a different perspective.
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: Bill S on 23/11/2017 14:45:57
Quote from: Colin
Firstly, it isn’t an infinitesimal pause it is genuinely a dt=0 at v=0. It is only infinitesimal if you choose to zoom out and sacrifice accuracy.

Are you saying that the stone does not actually stop?  Would that mean that the -ve > +ve acceleration happens at such low speed that the pause is only an illusion?
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: Bill S on 23/11/2017 17:06:46
Quote from: Yahya
I think the answer is : it spend at that point zero time

Just as an aside; what is the difference between being at a point for zero time, and not being there at all?
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: Colin2B on 23/11/2017 17:15:16
Are you saying that the stone does not actually stop?  Would that mean that the -ve > +ve acceleration happens at such low speed that the pause is only an illusion?
The answer is in @evan_au post #5.
Yes the stone does not stop because stopping implies spending time at a location in space. Yes, the pause is an illusion, as you say due to the low speed, also meaning the transition between up and down motion is seamless.
To suggest otherwise would mean there is a flat spot at the apex, and clearly there isn’t.

Just as an aside; what is the difference between being at a point for zero time, and not being there at all?
There is one for the philosophers.
However, it passes through that point so it must have been there  ;)
Or does it just kiss the apex and move on  ;D

EDIT: PS Here is another thought for you @Bill S - is it possible to say that any moving point (eg the tip of your nose as you walk down the street) spends any time at a particular point in space. If it does it is stationary. So, has your nose been anywhere?
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: Bored chemist on 23/11/2017 21:55:35
You can never divide by pure zero.
it's just my personal explanation.
Thanks for clarifying your lack of understanding.
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: Bill S on 24/11/2017 06:01:06
Quote
So, has your nose been anywhere?

Assuming that walking produces a continuous motion in a constant direction, it would seem that your nose does not stop.  Therefore, it spends no time at any specific point.  If every point along the way is designated as “a specific point”, it follows that your nose has spent no time at any point. So, if spending no time at a point (a) is the same as not being there (b), your nose has been nowhere.  Since we know that your nose has been somewhere, there must be a difference between a and b.

So far, so good; but how do you define the difference?  Consider the following: If points A, B and C are contiguous points along your way, there is no space between them.  Your nose spends no time at A, B or C. Between A>C there is nowhere for your nose to be, so how long does it take your nose to move from A to C.    If you extend this “journey”, say, from A to Z; does that make any difference to the time taken?

Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: Bill S on 24/11/2017 13:57:18
Another thought: If it takes your nose no time to travel from A to Z, it must travel at "c".  In order to do that, it must be massless.

There's no accounting for hooters.
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: geordief on 24/11/2017 14:36:34
"Keep a clean nose. Watch the plain clothes. You don't need a weatherman. To know which way the wind blows."

The model  is not the same thing as what is observed.It is like Aesop's  tortoise trying to catch up with the hare
Title: Re: How long does a stone thrown into the air spend stationary at the highest point?
Post by: Colin2B on 24/11/2017 15:16:34
"Keep a clean nose. Watch the plain clothes. You don't need a weatherman. To know which way the wind blows."
Look out kid
It's somethin' you did
God knows when
But you're doing it again

Hare today, gone tomorrow

Another thought: If it takes your nose no time to travel from A to Z, it must travel at "c".
Or instantaneous?