# Relativity question

1. Jan 20, 2006

### Tony11235

Melissa is on a flatcar moving east at 0.6c relative to Bob. She holds a flashbulb in each hand and causes them to flash simultaneously. Melissa's hands are 2.0 m apart and her arms are oriented in an east-west direction. According to Bob, which flashbulb flashes first and by how much?

For some reason I cannot get myself started on this problem. Any hints or help?

2. Jan 20, 2006

### Gamma

I have forgotten most of relativity that I learnt. But it is tempting to give it a try. So if I am wrong I hope some one will correct me here.

The time difference between the two light pulse must be caused by the separation of the light sources i.e 2m. However, Bob sees this length contracted due to length contraction

So for Bob, separation between the light sources = L' = L/gamma = 2/gamma

L' = 1.6 m ( gamma = 1.25)

So the time difference between the pulses = L' / c = 5.3 ns.

3. Jan 20, 2006

### Tom Mattson

Staff Emeritus
Gamma: Please don't give offer complete solutions to homework problems. We want students to do most of the work, and we help.

That said, I don't agree with your solution. In order for the 2.0m to be considered a length in Bob's frame he would have to measure the distance between Melissa's hands simultaneously. But if he uses the flashes to measure the distance he does not make the measurements simultaneously, because in his frame the flashes are not simultaneous.

Tony: Let Bob's frame be $S$ and let Melissa's frame be $S^{\prime}$. Let Event 1 be "East light flashes." and Event 2 be "West light flashes." Then begin as follows.

1.) Write down spacetime coordinates for Events 1 and 2 in $S^{\prime}$.
2.) Compute spacetme intervals from the coordinates found in 1.).
3.) Use the Lorentz transformation to find the time between the flashes in $S$.

4. Jan 20, 2006