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

[Macy]

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..

 

[Macy]

For my answer I got (.0078, .004725, 0,0) as my time and position coordinates... Is this correct?

 

[Macy]

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?

 

[PeroK]

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.

 

[Macy]

Also the train is moving at 0.6c