What trajectory would have a bullet if fired from equator in a straight line

[azoulay]

I think this is a simple question but I cannot find the answer on the Internet.

What trajectory would have a bullet if fired in a straight line towards space from the equator?

1- Assuming there is NO gravity involved,
2- Considering that the bullet is going at a constant velocity,
3- Considering the rotation of the Earth on itself.

I'm arguing with a colleague at work. He thinks the trajectory will be a straight diagonal but I think it's going to be an ellipse. Who's right?

Regards,

Jonathan

 

[nasu]

So there is no gravity. Is there any other force?
If not, the trajectory will be a straight line. An ellipse (or any other curved path) will require some force.

 

[DaveC426913]

Your riend is right.

As you say, there is no gravity.

The gun is moving East with a velocity of 1000mph.

The bullet will head upward at muzzle velocity and Eastward at 1000mph in a straight line.

I'm not sure why you eliminate gravity but there you have it.

 

[QuantumPion]

Are you ignoring air resistance too?

 

[AlephZero]

First, you have to decide how you are measuring the trajectory.

An observer at a fixed point on the Earth's surface (rotating around the Earth's axis) will "see" a different path from an observer at a "fixed point in space" (or more precisely, at rest in an inertial coordinate system).

Neither of them wlll observe an ellipse, unless you can think of a reason why the bullet will keep returning to the same place it was fired from.

The observer "fixed in space" will see motion in a straight line. THe observer stationary on the Earth's surface will see a spiral path with parts of the spiral invisible, because the Earth itself will be blocking the view.

Of course if there is no gravity, the Earth will still be rotating about its axis but the observer on the Earth's surface will have some serious problems trying to stay in one place.

 

[Studiot]

Surely this is one of those trick questions?

What trajectory...in straight line?

Well then your answer is defined in the question.

 

[azoulay]

Thank you for the replies, I didn't think this was a tricked question.

I'll refine my question a little bit and to answer some questions from the replies:

> So there is no gravity. Is there any other force?

The reason for the NO gravity is that we're only arguing in the trajectory of the bullet while it's moving upwards.

The only force that I thought was important in the upward trajectory of the bullet was the rotation of the Earth on itself. But maybe I'm mistaken ?

> The gun is moving East with a velocity of 1000mph.

That's a bit what we're arguing about. My friend seems to add 2 vectors: one going straight up to space (perpendicular to earth) and another vector going East and this one being PERPENDICULAR to the first vector. That is why he is concluding that the resultant will be a diagonal.

For me, I'm seeing the first vector the same way as he does, (going straight up to space perpendicular to earth) but I see the second vector differently. I see the second vector also going East but NOT being perpendicular to the first vector. This second vector, I see it as going East but it's a curved vector (because the Earth rotating on itself is a curved force).

So for me the trajectory of the bullet has to be a curved line (like a portion of an ellipse). I cannot understand how my friend could be seeing a diagonal trajectory because the Earth rotating on itself is a curved force.

> Are you ignoring air resistance too?

Would that make a difference between the trajectory being a diagonal or a curved line?

> First, you have to decide how you are measuring the trajectory.

I understand that two observers (one on earth, on in space) would see two different trajectory but is there a "REAL" trajectory notwithstanding the observers location ?

> Neither of them will observe an ellipse, unless you can think of a reason why the bullet will keep returning to the same place it was fired from.

What I meant was not an ellipse where the bullet would return to the same place it was fired but I meant that the trajectory would be a curved line going upward in the skies and also going East (because of the rotation of the Earth on itself)

> The observer stationary on the Earth's surface will see a spiral path

I don't understand how it could end up being a spiral path?


Regards,

Jonathan

 

[DaveC426913]

The reason for the NO gravity is that we're only arguing in the trajectory of the bullet while it's moving upwards.

The only force that I thought was important in the upward trajectory of the bullet was the rotation of the Earth on itself. But maybe I'm mistaken ?

Gravity affects its entire path. Gravity is what pulls its trajectory back to Earth.

That's a bit what we're arguing about. My friend seems to add 2 vectors: one going straight up to space (perpendicular to earth) and another vector going East and this one being PERPENDICULAR to the first vector. That is why he is concluding that the resultant will be a diagonal.

True.

For me, I'm seeing the first vector the same way as he does, (going straight up to space perpendicular to earth) but I see the second vector differently. I see the second vector also going East but NOT being perpendicular to the first vector. This second vector, I see it as going East but it's a curved vector (because the Earth rotating on itself is a curved force).

There is no such thing as a curved force.

The force acting on the bullet by the gun is tangential to the gun's curved path. The only point of concern on the gun's path is the instant the bullet leaves it. And at that point, the force is due East. Once the bullet leaves the gun, there is no force acting on the bullet. In particular, there is no force moving it Eastward, or along the Earth's rotation. It will proceed along the same straight path unless acted upon by another force. The only forces left are gravity or air resistance. If you rule them out, the bullet goes straight.

See attached diagram.

I understand that two observers (one on earth, on in space) would see two different trajectory but is there a "REAL" trajectory notwithstanding the observers location ?

No. There' no "real" trajectory. However, the observer hanging in space will be able to account for all forces acting on the object without having to invent fictitious forces to explain the bullet's path. The observer on the Earth will see some odd curvature - not because the bullet's path is curving away from the observer - but because the observer's path is curving away from the bullet!

I don't understand how it could end up being a spiral path?

If the bullet rises away from the observer while the observer spins underneath (over days or weeks) the observer will see the bullet diappear over the horizon and reappear ever farther way with each reappearance (a half day later). To him, it will apear as if the bullet is climbing a long spiraling path away from Earth.

 

[azoulay]

I also got a diagram ) I wasn't expecting that bonus.

Thank you very much for all these precise answers, now my colleague's laughing at me but that's alright.

Seems to me so strange that's things are working that way. It is to me counter intuitive.

I'm guessing all that theory relies entirely on Newton's first law of motion?

Is there any experiments that were done were we can actually see from our eyes that diagonal path ? (The theory makes sense but I would like to see it with my own eyes.)

Thanks so much,

Jonathan

 

[azoulay]

I forgot to ask a question in my last post:

Why is Newton's law of inertia only an hypothesis ?

thanks again,

Jonathan

 

[DaveC426913]

Is there any experiments that were done were we can actually see from our eyes that diagonal path ? (The theory makes sense but I would like to see it with my own eyes.)

Well, you could ride your bike due north and fire off a pingpong gun due West. Can you see any reason why the ping pong ball would not follow a straight line somewhere Northwest?

Even if, instead of due North, you rode around in a circle, it would not affect the path of the ping pong ball. The ping pong ball's path is set the moment it leaves the barrel, and its direction s determined only by the instent it leaves the barrel, not what preceded that.

 

[Cleonis]

I forgot to ask a question in my last post:
Why is Newton's law of inertia only an hypothesis ?

Well, to state that 'Newton's law of inertia is only a hypothesis' is trying to be more Catholic than the Pope.
The phenomenon of inertia is as certain as it gets.


That said, it is necessary to be cautious. In the history of physics there have been cases where a phenomenon was thought of as being firmly established - and then a counterexample surfaced.

Example:
For many years parity conservation was considered to be a principle of physics. (It's not important here what exactly 'parity' is, so I won't go into parity here.) in 1956 someone obtained the funds to set up an experiment which would check parity in a situation where it hadn't been checked before. To everyone's surprise it was found that the law of parity conservation didn't apply in the circumstances that were investigated in that experiment.

Physicists have learned from the surprises in the past. No matter how long a principle has stood the test of time, there is always a possibility that some day you find in the course of some experiment that it's not a fundamental principle after all.

 

[azoulay]

Thank you very much for all the answers to my questions.

Jonathan