All Problems

Relativistic Mechanics

Problem 1.351

Two unstable particles move in the reference frame \(K\) along a straight line in the same direction with a velocity \(v=0.990 c\) The distance between them in this reference frame is equal to \(l\) \(=120 \mathrm{~m} .\) At a certain moment both particles decay simultaneously in the reference frame fixed to them. What time interval between the moments of decay of the two particles will be observed in the frame \(K ?\) Which particle decays later in the frame \(K ?\)

Reveal Answer
1.351. The forward particle decayed \(\Delta t=l \beta / c\left(1-\beta^{2}\right)=20 \mu \mathrm{s}\) later, where \(\beta=v / c\)