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I am a superman [:D] . I lift a helicopter from earth and go a certain height above the earth . Then i wait for earth to rotate , and soon america comes right below me and i come down . Hence i reach america .
Is this possible ??
Assume that america does come under me for sure , wherever be my original position and also assume that i have a lot of time [:)]
Comments (45)
and im not trying to be "veryyyyyyyyyyyyyyyy precise".. im jus talkin of the fundas..and i fail to understand y an expert is trying to challenge me to solve some complex diff eqn.. if v students cud do all tht then wat r u experts there for???
no offence to any expert..
bcoz when the superman was on earth its W(ang . vel) was equal to that of earth..
now when he lifts up the tangntl vel. remains same as that on the ground b4 , but since the ang. vel decreases bcoz the radius frm the centre to the man bcoms > than radius of earth ...
so as long as he remains at some height abv the grnound ,his angular vel.W remains smaller than that of the earth..
so the place benteath him constantly keeps changing and he DOES NOT REACH THE SAME PLACE AS B4...
except in one case when the time of arrivaal is such that earth has completed one full roration.. and the place benath him after changing constantly has come to the same place due to the full rotation of the earth.....
@ computer .
Let's be serious !!
First of all , the analogy by which u are drawing conclusion is ENTIRELY FALSE . That's because in the merry - go-round u don't have any appreciable gravitational force towards it . But in the problem u HAVE TO CONSIDER the gravitational force on the helicopter or whatever .
So now explain ur reasoning .
I think now it would be clear to u why I was telling to solve the differential eqn of motion . Got it ?
Now the problem can be formulated as follows:
Consider a ball given an upwards velocity v wrt earth which is rotating at a constant angular speed w. Find the time when the ball hits the Earth again .Also find the angular displacement of the ball on hitting the earth .
If earth moves by same amount by the same time then it will land at the same point , otherwise not .
Do u agree with this formulation ? If agree then plz go ahead using spherical polar co-ordinates . That's not so difficult but may be time-consuming ,
Anyway , I am pleased with ur clear-cut comment . An academic comment , I believe( Unlike some experts ),should be made like this .
Anyway ,after some calculation in polar co-ordinates I have obtained the final differential eqn in the formulated problem as follows:
The initial conditions are at t=0, r=R and 
where R is the radius of the earth , M = mass of the earth and v is the velocity at which it was initially thrown up into the air ,wrt earth .
Now we have to solve this eqn to find the non-zero time when r=R .
And then proceed in the way in my previous post .
See, the differential eqn is not difficult itself but the calculations are a bit lengthy .
To solve it , u may put p = dr/dt
so LHS = pdp/dr
Now integrate both sides wrt r .
Then find p ( = dr/dt).
Then solve r(t) .( all the initial conditions are specified )
Please someone try it !!!
Anybody consider Coriolis Force?? It will add a small component in the tangential direction during the motion, and so even if he does not land in USA he will not land back in the same place.
I am surprised that the Forum Expert has not even mentioned it.
A frank observation on reading all these replies is that Forum Expert hardly seems to have his fundas right. And he is not civil enough while answering the questions
And Mr.Computer001's questions have not been addressed properly at all.
Newton's Law tells us that a body continues to be in a state of uniform motion or rest in an inertial frame unless acted upon by a force. A rotating body is not in a state of uniform motion as the direction of velocity is not constant. So, to keep the body in circular motion, a force has to be supplied to maintain it in a circular path. This is the centripetal force
On earth, this force is gravity. In fact gravity is very dominant compared to the centrifugal force and this remains true to a considerable height. So, the heli will actually still remain in circular motion. In the merry-go-round example or a turn-table, the friction and the normal reaction provided by the seat and the wall are absent as soon as the man loses contact. So he will now move in a tangent. Not so in the heli example.
Now, does a tangential force act? This is where I am surprised that the expert has explicitly stated that there is no such force. Whenever a body moves in a rotating frame with a radial velocity, a force arises in the tangential direction. It is called the Coriolis Force and the acceleration is given by 
So, this force causes a displacement proportional to the velocity of the body in the same sense as the rotating frame.
So, our request to Superman, on your way up to a reasonbale height, be quick and on your way down, come down gently!
To @phystud
Get ur fundas right Man !!!!!!!!!.
Do u know a piece of information that the so-called centrifugal force is NOT a kind of actual force and we can live happily without even considering it ?
Surprised ?
U should be !!!!!!!!
See ,centrifugal force acts when u are in a non-inertial frame ( i.e. U are soving an eqn. of motion residing in such an non-inertial frame ) and corriolis force acts when the Body has a velocity wrt the non-inertial rotating system residing entirely with it . ( I suspect whether u can understand these or not , otherwise such a silly response is not expected from u !!! ) .
And all my discussion and eqn that I have already posted is wrt an inertial ref frame and in no case should the corriolis force should come into the picture as the body has left the contact from the rotating earth !!
Do u get it ? Or need further explanation .
Anyways , I think u should re-read the portion of corriolis force and frames of refernce from Atleast resnick - Halliday as u would find them less confusing .
Anyways ,all the best !!
Crap and nonsense!
The body has a radial velocity w.r.t to the earth while rotating about the centre of the earth. It will experience the Coriolis Force. Also, I feel your fundas as far as pseudo forces go need some revision.
The confusion is arising because of failure to address Computer001's doubt correctly. If you had paid attention to the fact that the helicopter is still rotating, you would not have had this misapprehension.
Your call.
The Coriolis force appears in the frame of the earth and hence the body alights a small distance away.
I suspect you have never done a problem of a body released a few hundred metres above the ground to calculate the deflection due to the Coriolis Force
And have you heard of Focault's Pendulum whose operating principle is partly the Coriolis Force.
Do not misguide students in this way. Pay attention to what they are asking in their eagerness to learn!
I can only say a word :
" Write a book so that we student ( as well as late Resnick , Halliday , Irodov etc) can benefit from it ."
Also I can't argue with u indefinitely ( time constraint !! ) because an argument can only go on if both of us go on with a logical line and u certainly are not playing ur part fairly ( sorry to saythis);
If u think that I am misguiding the student then plz don't be 'misguided' (:( My humble request )
Anyway , continue with ur own fundas and u will surely win a nobel prize one day as they are now looking for some crazy ideas .
On a final note (and serious) : Can u plz rewrite my formulated problem in ur own words ?( so that we could know that we are dealing with a person who understands how to read mechanics problems )That' s very important and don't take it otherwise .
Anyways u can continue with all ur slangs and I don't mind it !
i think the derivation of the eqn will giide u right .
we have in polar co-ordinates
................................(1)
again the angular momentum remains constant
so we get
.......................................(2)
Now eliminating the derivative of theta from (1) and (2) I get this eqn .
The initial conditions are dr/dt = v ( the initial velocity at which the body is thrown upwards ) and r=R
as the body was initially at ground .
Do u understand those ?
After all these exchanges of words the confusion is stil there about Coriolis force in the present example.
In a rotating system like earth when a body falls down or goes up vertically with a velocity say ' v ' the coriolis force will be 2 v 
. So when helicopter goes up if v is reasonably high coriolis force will act is n't it? This force affects even flow of winds. Superman and helicopter is part and parcel of earth's rotating syatem unless he takes off with escape velocity. I feel if superman goes up and down in same speed the effect of Coriolis will get nullified and he will land in the same position.
I think we should continue the discussion and more experts should join this thread for a healthy discussion and correct conclusion!!
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ofcourse im talkin abt jumping to a high enuf height...otherwise wats the pt of discussing this topic???
if it was some negligible height, then anchit cud have jus jumped and got his answer!!
n im only interested in the logic and reasoning not interested in solving..