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A muon at rest decays in 2.2 μs. Moving at 99.00% the speed of light, it would be seen to "live" for how long?

A) 0.66 μs
B) 1.10 μs
C) 2.20 μs
D) 4.39 μs
E) 8.79 μs

User Yoke
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1 Answer

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Final answer:

The muon would be seen to "live" for approximately 4.39 μs when moving at 99.00% the speed of light.

Step-by-step explanation:

The muon's lifetime in its frame of reference is 2.20 μs. When moving at 99.00% the speed of light, time is dilated, or stretched, due to relativistic effects. We can use the concept of time dilation to find how long the muon would be seen to "live" by an observer on Earth. The time dilation formula is given by:

t' = t / √(1 - v^2/c^2)

Substituting the given values:

t' = 2.20 μs / √(1 - 0.9900^2)

t' ≈ 4.39 μs

Therefore, the muon would be seen to "live" for approximately 4.39 μs.