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Two particles moving in a laboratory frame of reference along the same straight line with the same velocity v=(3//4)c strike against a stationary target with the time interval Deltat=50ns. Find the proper distance between the particles prior to their hitting the target. |
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Answer» SOLUTION :In the frame K in which the particles are at rest, their positions are A and B whose coordinates may be taken as, `A: (0, 0, 0), B=(l_0, 0, 0)` In the frame `K^'` with RESPECT to which K is moving with a velocity v the coordinates of A and B at TIME `t^'` in the moving frame are `A=(vt^', 0, 0) B=(l_0sqrt(1-beta^2)+vt^',0,0), beta=v/c` Suppose B hits a stationary target in `K^'` after time `t_B^'` while A hits it after time `t_B+Deltat`. Then, `l_0sqrt(1-beta^2)+vt_B^'=v(t_B^'+Delta t)` So, `l_0(vDelta t)/(sqrt(1-v^2//c^2))` 
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