Worked example: Muons are created 10 km up, moving at v = 0.998c toward the ground. Their proper lifetime is τ₀ = 2.2 μs. Do they reach the ground? Step 1: Without relativity: distance = c × τ₀ ≈ (3×10⁸)(2.2×10⁻⁶) = 660 m — far short of 10 km. Step 2: Compute γ = 1/√(1 − 0.998²) = 1/√(0.003996) ≈ 15.8. Step 3: Dilated lifetime in Earth's frame: τ = γτ₀ ≈ 15.8 × 2.2 μs ≈ 34.8 μs. Step 4: Distance covered = 0.998c × 34.8 μs ≈ 10,400 m ≈ 10.4 km > 10 km. Conclusion: time dilation lets them just reach the ground — confirmed by experiment, and the muon's own frame agrees via length contraction (10 km / 15.8 ≈ 630 m of atmosphere).