# Relativity problem.

1. Dec 19, 2004

### Rioluany

In a particular reference frame, two events occur 100m apart, with an intervening time interval of 0.30us . The speed of a reference frame in which they occur simultaneously is ?

anyone can tell me how to slove this problem? I dont have any idea about it . Thanx

2. Dec 19, 2004

### ComputerGeek

you need to find a frame of reference where the time interval between events becomes zero.

3. Dec 19, 2004

### Andrew Mason

Let the occurence of event A have coordinates (x,y,z,t) = (0,0,0,0) in this frame, f. Event B will have coordinates (x_B,y_B,z_B,t_B) = (100,0,0,.30) (times in us.)

Consider another frame of reference, f', moving parallel to the direction of the displacement between Event A and Event B with speed v and with its origin at Event A (i.e in this frame the coordinates of Event A are (x',y',z',t') = (0,0,0,0))

We want to set v so that the coordinates of Event B in f' are $(x'_B,y'_B,z'_B,t'_B) = (x'_B,0,0,0)$

Times and distances in these frames are related by the Lorentz transformation:

(1)$$t'_B = \gamma (t_B - vx_B/c^2)$$
(2)$$x'_B = \gamma (x_B - vt)$$

So determine v if:
$$t_B' = 0$$

AM

Last edited: Dec 19, 2004