# Calculating Ice Cube Landing Points Using Galilean Relativity

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In summary, two trains, A and B, are traveling at constant speeds on parallel straight lines. Train A is moving at 5m/s and train B is moving at 2m/s. At a given instant, an observer at the station and passengers in both trains are aligned along a line perpendicular to the trains' motion. A passenger in train A drops an ice cube from a height of 1.40m. Using Galilean relativity, the ice cube will land at the same position for the passenger in train A, as there is no horizontal velocity of the cube relative to the train. To find the position for the observer at the station and the passenger in train B, the time it takes for the ice cube to
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2 trains are traveling at constant speeds on 2 parralel straight line. The first A is traveling at 5m/s the second B is traveling at 2 m/s. An observer at the station observes both trains. At a given instant of time, a passenger in A, a passenger in B and the observer at the sation are all aligned along a line normal to the motion of the trains. At that point, a passenger in A drops an ice cube from his drink which he is holding at a height of 1.40m. Using Galilean relativity where will the ice cube land as far as each observer is concerned?

I worked out for A to be x' + u't' = 0 as u' = 0 as there is no horizontal velocity of ice cube relative to A.

Im not sure of the formula to work out B and for ground observer can someone help?

any ideas would be useful, I am not sure whether I am expected to work out the time of how long it will take for the ice cube to land using the distance 1.4 m and gravity?

Yes, they expect you to work out the time using gravity and the initial height of the cube, then use Galilean coordinate transformations on this (you could also work out the problems with the cube having an initial velocity equal to the relative velocities, but it sounds like they want you to explicity start with a Galilean transformation, so that you get a feel for how to use Lorentz transformations later on).

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any ideas anyone?

is my method for the asnwer for observer A correct??

## 1. What is the Galilean relativity problem?

The Galilean relativity problem refers to the discrepancy between Galilean relativity and the principles of special relativity. Galilean relativity states that the laws of physics are the same in all inertial frames of reference, while special relativity introduces the concept of the speed of light being constant in all inertial frames. This poses a problem when considering the transformation of velocities between frames.

## 2. How did Galileo contribute to the understanding of the Galilean relativity problem?

Galileo's experiments with falling objects and projectiles led to the development of the principle of relativity, which states that physical laws and measurements are the same in all inertial frames of reference. This idea later became the basis for Galilean relativity and the subsequent problem it posed for special relativity.

## 3. Why is the Galilean relativity problem important in modern physics?

The Galilean relativity problem highlights the limitations of Galilean relativity and the need for a more comprehensive theory, which led to the development of special relativity. It also plays a key role in understanding the fundamental principles of relativity and their implications for our understanding of the universe.

## 4. How does the Galilean relativity problem affect our everyday lives?

While the effects of special relativity are negligible in our daily lives, the Galilean relativity problem has practical applications in fields such as aeronautics, where the transformation of velocities between frames is crucial for accurate calculations and measurements. It also has implications in other areas such as GPS technology.

## 5. What solutions have been proposed for the Galilean relativity problem?

One solution is to abandon the principle of relativity and accept that there is a preferred frame of reference where the speed of light is constant. However, this contradicts the fundamental principles of relativity. Another solution is to modify Galilean relativity by introducing a "preferred" frame of reference, but this also conflicts with experimental evidence. The most widely accepted solution is to embrace the principles of special relativity and understand that the transformation of velocities between frames is a necessary consequence of the constant speed of light.

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