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

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Homework Help Overview

The problem involves calculating space-time coordinates related to a scenario where Derick, fleeing from the police, throws drugs from a car on a relativistic train. The context includes the use of Lorentz transformations to relate the events observed by the police to those occurring in Derick's frame of reference.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of Lorentz transformations and the correct velocities to apply in these transformations. There is uncertainty regarding the proper reference frames and whether the velocity of the train or the drugs should be used.

Discussion Status

Some participants are attempting calculations and sharing their results, while others express confusion about the problem setup and the appropriate application of relativistic concepts. There is an ongoing exploration of the assumptions made regarding velocities and reference frames.

Contextual Notes

Participants note the unspecified speed of the train and the need for clarity on the events described in different frames. The problem involves multiple reference frames, which adds complexity to the discussion.

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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For my answer I got (.0078, .004725, 0,0) as my time and position coordinates... Is this correct?
 
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?
 
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.
 
Also the train is moving at 0.6c
 

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