Train traveling at relativistic speeds - Finding velocity.

• chris_0101
In summary, the question asks for the speed of the eastbound train with respect to the westbound train, based on the Galilean and Relativistic velocity transformation equations. The answer is 0.5c, as calculated from the given velocities of 0.6c and 0.8c for the westbound and eastbound trains respectively. The ticket taker's speed is not a factor in this calculation. The concept of time dilation may suggest a decrease in velocity as one approaches the speed of light, but this is not directly relevant to the question.
chris_0101

Homework Statement

Two trains leave a station, one going westbound and one going eastbound, both on the same track. A passenger who just wanted to get out of town missed both trains and, while standing on the platform at the edge of the track, observes the westbound train to be receding at 0.6c and the eastbound train to be going 0.8c. There is a very efficient ticket taker on the westbound train going from the back to the front of her train at 0.4c (this is relative to seated passengers on her train, of course)! For both the Galilean and Relativistic velocity transformation equations what would be the speed of the eastbound train with respect to the westbound train (call it ur) according to the observer at the station?

Homework Equations

u'=(v-u)/(1- vu/c^2 )

Where:
u' is the speed of the train relative to the station observer
v is the speed of the observer relative to the westbound train
u is the speed of the speed of the eastbound train relative to the westbound train

The Attempt at a Solution

I am asking for a "second opinion" I guess you could say. The value that I calculated is 0.5c. I am still trying to wrap my head around these concepts and I am uncertain that if one approaches the speed of light, does the speed of that person (or train in this case) will decrease.

As a side note, I have a strong belief that velocity does decrease due to the fact that time dilates or increases as one approaches the speed of light. If this is true, then the velocity should decrease.

I think that this is a trick question because all the velocities are already given from the perspective of the observer on the platform and he can only calculate their velocities relative to one another mathmatically and not measure them directly (he is not on the train). The ticket taker is a distraction. They are moving away from each other 1.4c, but that is fine because it is not a directly measured velocity but derived from 2 separate measurements.

1. What is the theory of relativity?

The theory of relativity is a scientific theory developed by Albert Einstein in the early 20th century. It consists of two theories - the special theory of relativity and the general theory of relativity - which describe how the laws of physics behave in different frames of reference.

2. How does the theory of relativity apply to train traveling at relativistic speeds?

According to the theory of relativity, the laws of physics are the same for all inertial observers. As a train approaches the speed of light, it experiences time dilation and length contraction, meaning that time and distance appear to be different for observers on the train compared to those on the ground. This is due to the train's velocity approaching the speed of light relative to the observers on the ground.

3. How does one calculate the velocity of a train traveling at relativistic speeds?

The velocity of a train traveling at relativistic speeds can be calculated using the formula v = c * tanh(r), where v is the velocity of the train, c is the speed of light, and r is the ratio of the train's velocity to the speed of light. This formula takes into account the effects of time dilation and length contraction.

4. What is the significance of traveling at relativistic speeds?

Traveling at relativistic speeds allows for objects to experience time differently and to travel vast distances in a shorter amount of time. This has implications for space travel and could potentially lead to the development of technologies such as time travel.

5. Are there any limitations to traveling at relativistic speeds?

As an object approaches the speed of light, its mass also increases according to the theory of relativity. This means that it would require an infinite amount of energy to accelerate an object with mass to the speed of light. Additionally, at such high speeds, even small particles can cause significant damage to the object, making it difficult to protect it during travel.

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