Calculating Space-Time Coordinates for Derick's Drug Toss on Relativistic Train

In summary: I think, not 0.6.In summary, the problem involves a drug dealer, Derick, fleeing from the cops on a relativistic train. The cops see Derick leaving the back of the train and arriving at the front of the train in 0.00775 seconds, while he throws drugs at -0.6c relative to himself when he reaches the middle of the train. The question is what are the time and position coordinates of when the drugs reach the end of the train in the police's reference frame. The solution involves using Lorentz transformations and the velocity addition equation to find the velocity of the drugs with respect to the train. The answer obtained was (.0078, .004725, 0,0
  • #1
Macy
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Homework Statement


Derick is fleeing from the cops on a car on a relativistic train. At xr= 0.0m and tr =0.000s the cops at rest see Derick leaving the back of the train and head towards the front of the train on his relativistic car. The cops see him arrive at the front at xr = 1.875*10^5m and tr= 0.00775 seconds. When Derek reaches the middle of the train he throws his drugs at -.6c relative to himself. What are the time and position coordinates of when the drugs reach the end of the train in the police's reference frame?

Homework Equations


Lorentz transformations
Xm =( Xr -vtr)gamma
Tm=(Tr-vxr)gamma
v(in the rest frames reference )= (Vm+ Vme(respecttoearth))/1+Vm(Vme)

The Attempt at a Solution


So first I found the length of the train which I thought to be 600,000 meters and then I used the velocity addition equation to find the velocity of the drugs with respect to the train to get the space-time coordinates but my answer is not coming out right..
 
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  • #2
For my answer I got (.0078, .004725, 0,0) as my time and position coordinates... Is this correct?
 
  • #3
I am not sure if I used the right velocity for the Lorentz transformations? For all the transformations from the moving to the rest frame you would use the velocity of the train?
 
  • #4
Macy said:
I am not sure if I used the right velocity for the Lorentz transformations? For all the transformations from the moving to the rest frame you would use the velocity of the train?
I'm not sure I understand the problem. There's a train traveling at some unspecified speed. There's a drug dealer in a car on the train, moving inside the train? There are some events described in the cop's (rest) frame, subscripted by ##r##. And there are drugs thrown by the drug dealer at a given velocity in his frame.

You need a diagram to sort that lot out.
 
  • #5
Also the train is moving at 0.6c
 

1. What is the Lorentz transformation?

The Lorentz transformation is a mathematical formula used to relate the measurements of space and time between two different frames of reference in special relativity. It describes how measurements of time and distance change when an observer is moving at a constant velocity relative to another observer.

2. Why is the Lorentz transformation important?

The Lorentz transformation is important because it is a fundamental concept in special relativity, which is a crucial theory in modern physics. It helps us understand how space and time are relative and how they are affected by the speed of an observer.

3. How do you derive the Lorentz transformation?

The Lorentz transformation is derived from the postulates of special relativity, which state that the laws of physics are the same for all inertial observers and that the speed of light is constant for all observers. By using these postulates and mathematical equations, the Lorentz transformation can be derived.

4. Can you explain the difference between a Lorentz transformation and a Galilean transformation?

A Galilean transformation is a mathematical formula used to relate measurements of space and time between two frames of reference in classical mechanics, where the laws of physics are the same for all observers. However, a Lorentz transformation takes into account the effects of the speed of light and is used in special relativity, where the laws of physics are the same for all inertial observers, but the speed of light is constant for all observers.

5. What are some real-world applications of the Lorentz transformation?

The Lorentz transformation has many real-world applications, including in particle accelerators, where it is used to calculate the effects of relativistic speeds on particles. It is also used in GPS systems, as it accounts for the effects of time dilation on satellites in orbit. Additionally, the Lorentz transformation is used in the development of theories and technologies related to space travel and time travel.

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