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(a) Two particles are created in a high-energy accelerator and move off in opposite directions. The speed of one particle, as measured in the laboratory, is 0.650c, and the speed of each particle relative to the other is 0.950c. What is the speed of the second particle, as measured in the laboratory? (b) The positive muon (u*), an unstable particle, lives on average 2.20 x 10-6 s (measured in its own frame of reference) before decaying. (i) If such a particle is moving, with respect to the laboratory, with a speed of 0.900c, what average lifetime is measured in the laboratory? (ii) What average distance, measured in the laboratory, does the particle move before decaying?

(a) Two particles are created in a high-energy accelerator and move off in opposite directions. The speed of one particle, as measured in the laboratory, is 0.650c, and the speed of each particle relative to the other is 0.950c. What is the speed of the second particle, as measured in the laboratory? (b) The positive muon (u*), an unstable particle, lives on average 2.20 x 10-6 s (measured in its own frame of reference) before decaying. (i) If such a particle is moving, with respect to the laboratory, with a speed of 0.900c, what average lifetime is measured in the laboratory? (ii) What average distance, measured in the laboratory, does the particle move before decaying?

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(a) Two particles are created in a high-energy accelerator and move off in opposite directions. The speed of one particle, as measured in the laboratory, is 0.650c, and the speed of each particle relative to the other is 0.950c. What is the speed of the second particle, as measured in the laboratory? (b) The positive muon (μ⁺), an unstable particle, lives on average 2.20 × 10⁻⁶ s (measured in its own frame of reference) before decaying. (i) If such a particle is moving, with respect to the laboratory, with a speed of 0.900c, what average lifetime is measured in the laboratory? (ii) What average distance, measured in the laboratory, does the particle move before decaying?
Transcribed Image Text:(a) Two particles are created in a high-energy accelerator and move off in opposite directions. The speed of one particle, as measured in the laboratory, is 0.650c, and the speed of each particle relative to the other is 0.950c. What is the speed of the second particle, as measured in the laboratory? (b) The positive muon (μ⁺), an unstable particle, lives on average 2.20 × 10⁻⁶ s (measured in its own frame of reference) before decaying. (i) If such a particle is moving, with respect to the laboratory, with a speed of 0.900c, what average lifetime is measured in the laboratory? (ii) What average distance, measured in the laboratory, does the particle move before decaying?
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