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Consider a radioactive nucleus that moves with a constant speed of 0.5c relative to the laboratory....

  1. Consider a radioactive nucleus that moves with a constant speed of 0.5c relative to the laboratory. The nucleus decays, emitting an electron with a speed of 0.9c relative to the nucleus and along its direction of motion.
  2. Find the velocity of the electron in the laboratory frame.

  3. Suppose now that the nucleus decays by emitting an electron with a speed of 0.9c, but in a direction perpendicular to its direction of motion as determined by an observer at rest with respect to the nucleus.

  4. Write down the components ux and uy of the electron’s velocity in the laboratory frame.
  5. Calculate the magnitude of u and its direction relative to the laboratory frame.
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