# Homework Help: * Using Lorentz transform to find velocity of rod

1. Oct 2, 2007

### Odyssey

URGENT* Using Lorentz transform to find velocity of rod

1. The problem statement, all variables and given/known data
a person at the origin of an inertial reference frame S observes a rod of proper length l moving towards him at a speed v. He notes that the rod takes a time T to pass him. Assuing that when the front end of the rod passes the observer, the clocks in S and in the rest frame S' of the rod are both set to read zero. Using Lorentz transformation, establish a relation between the coordinates of event E2 to find the velocity of the rod. E2 is when the tail end of the rod passes the observer at the origin S.

2. Relevant equations
The lorentz transformation equations...and its inverse perhaps?

3. The attempt at a solution
I think I identified the coordinates alright...here they are (I hope):
T is the proper time measured by S, so for E2, S measures (x,t)=(0,T).
Time is dilated for S' (rest frame of moving rod), so for him E2 is at (0,gamma*T)

So now I have to use the Lorentz tranformation...but how...? to solve for the velocity of the rod...in terms of l...and T...?

Thanks for the help in advance...I greatly appreciate it. Assignment is due VERY soon. Friend said he was going to help me but didn't. :(

2. Oct 2, 2007

### Gokul43201

Staff Emeritus
It x' = 0 for E2? Note: You want to set x'=0 for E1.

Once you've correctly written (x,t) and (x',t') for E2, what invariance can you use to relate these quantities?

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