A muon formed high in Earth's atmosphere travels at a speed 0.960c for a distance (as we see it)of 4500 m before it decays.How far does the muon travel as measured in its frame?
A)2520 m
B)16,100 m
C)4320 m
D)1260 m
E)4500 m

Question

A muon formed high in Earth's atmosphere travels at a speed 0.960c for a distance (as we see it)of 4500 m before it decays.How far does the muon travel as measured in its frame?
A)2520 m
B)16,100 m
C)4320 m
D)1260 m
E)​4500 m

Quizplus · Accepted Answer

The distance traveled by the muon in its own frame can be found using the length contraction formula: $L = L_0\sqrt{1-v^2/c^2}$, where $L_0$ is the length measured in the stationary frame (4500 m), $v$ is the velocity of the muon (0.960c), and $c$ is the speed of light. Plugging in the values, we find that the length contracts in the muon's frame, resulting in a shorter distance traveled than what is observed from Earth. The correct calculation leads to approximately 1260 m, making option D the correct answer.

A Muon Formed High in Earth's Atmosphere Travels at a Speed