If you immediately see that the cart running on the treadmill is doing exactly the same thing as the cart moving along the ground in the wind, you are a whole leap ahead of many people who can't/won't accept this, equations or not.
Your example does not go in a circular path. As jtbell says, the path will consist of four parabolic segments.
If an object does go in a circular path at a constant speed, then it is by definition in uniform circular motion. In this case, the acceleration of the object will always be towards...
If you include the Earth in your system, momentum is conserved: the change in momentum of the car is equal and opposite to the change in momentum of the Earth. It's just that nobody will notice the change in momentum of the Earth. Since the Earth is so massive, the change in its velocity will be...
You can still define a reference frame to be at rest with respect to A, or one that is at rest with respect to B. You can also define a reference frame to be moving at a velocity x with respect to A, or one that moves at velocity y with respect to A, or one that moves at velocity z with respect...
You've just repeated the same question. I already said this:
Just replace "missile" by "person" and the same thing applies. The whole point of relativity is this: all motion is relative. You want to know how I can tell if it is A that is moving towards me or me that is moving towards A. The...
It is equally valid to say that A is moving towards B as it is to say that B is moving towards A. We cannot say in an absolute sense that one of the missiles is "moving" and the other is "at rest": we can only say that there is relative motion between the missiles.
If I am sitting on one of...
Remember that "at rest" has no meaning in an absolute sense: you can only say that something is "at rest" with respect to something else. You use the phrase "when reference frame is at rest". This phrase as it stands has no meaning.
This is unclear. You say "as both the objects are moving"...
Have a look at the wikipedia article on Faster-than-light, "closing speeds"
See also the paragraph on third party observers on this page: Is Faster-Than-Light Travel or Communication Possible?.
The speed of one photon relative to another one is undefined, since a photon does not define a reference frame. You can replace the photons by objects traveling as near to the speed of light as you wish (see my example above): their relative speed will never be above c.
I must once more...
Yes, as already stated, the closing rate (being the rate of change of the distance measured between the two objects) as seen by the observer in this frame is 1.98c. That is not the same thing as the speed of one object with respect to the other one.
The fact that "closing rate" and "relative...
The "cosmic speed limit" applies to objects with mass relative to an inertial frame.
Instead of photons, imagine two massive objects approaching each other. Each object has a speed of 0.99c relative to the observer between them. This observer can calculate that the distance between the two...
mananvpanchal, I'll just point out one problem with your analysis above:
You have transformed the coordinates of the event when the platform observer perceives the two rope pulls into the frame of the train observer. Now you have the coordinates of the event "platform observer perceives rope...
If non-relativistic calculations are used, the train observer will calculate that the two events are also simultaneous in his frame. It is only by using relativistic calculation that you will get a different result for the time coordinate of the two events in the train frame. If the calculations...
The forces of lift and drag will act through the centre of pressure, not the centre of mass. NASA has an excellent series of pages on kite aerodynamics. Here's the one about centre of pressure.