QCE Vault / Physics Special relativity — Question 34 Original QCE Vault practice · 1 mark
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QUESTION 34 Muons have a proper mean lifetime of 2.2 μ s 2.2\,\mu\text{s} 2.2 μ s and travel at 0.995 c 0.995c 0.995 c relative to Earth. Approximately how far can a typical muon travel in Earth’s frame during one dilated lifetime? (A) 0.66 km 0.66\,\text{km} 0.66 km (B) 2.2 km 2.2\,\text{km} 2.2 km (C) 6.6 km 6.6\,\text{km} 6.6 km WORKED SOLUTION
Answer C 1 mark Worked solution
γ = 1 / 1 − 0.995 2 ≈ 10.0 \gamma=1/\sqrt{1-0.995^2}\approx10.0 γ = 1/ 1 − 0.99 5 2 ≈ 10.0 , so t ≈ 22 μ s t\approx22\,\mu\text{s} t ≈ 22 μ s . Then d = v t = ( 0.995 ) ( 3.0 × 10 8 ) ( 22 × 10 − 6 ) ≈ 6.6 × 10 3 m d=vt=(0.995)(3.0\times10^8)(22\times10^{-6})\approx6.6\times10^3\,\text{m} d = v t = ( 0.995 ) ( 3.0 × 1 0 8 ) ( 22 × 1 0 − 6 ) ≈ 6.6 × 1 0 3 m . Select the correct option.
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