How fast must a muon be moving if it looks to an observer at rest that it lived for 2 * 10 ^- ⁴ seconds before it decayed when, in fact, it lived for only 2 *10 ^- ⁶ seconds in its moving reference frame? A) 0.05c B) 0.50c C) 0.95c D) 0.995c E) 0.99995c

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Quizplus · Accepted Answer

The correct answer is E because the time dilation equation is: t' = t / γ, where t' is the time measured in the moving frame, t is the time measured in the stationary frame, and γ is the Lorentz factor. In this case, t' = 2 × 10^-6 s and t = 2 × 10^-4 s, so γ = t / t' = 100. The Lorentz factor is given by: γ = 1 / sqrt(1 - v^2 / c^2), where v is the velocity of the muon and c is the speed of light. Solving for v, we get: v = c * sqrt(1 - 1 / γ^2) = 0.99995c.

How Fast Must a Muon Be Moving If It Looks