Question

(15%) Problem 8: Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon that has speed v = 0.92c. The muon then travels at constant speed and lives 1.5 us as measured in the muon's frame of reference. (You can imagine this as the muon's internal clock.) Randomized Variables y = 0.92 c t = 1.5 us > * 33% Part (a) How long does the muon live in seconds) as observed on the Earth? At= Grade Summary Deductions 0% Potential Late Work % 100% Late Potential 100% 10046 7T ( 7 8 9 HOME E sin cos tan cotan asino acos atano acotano cosh tanh cotanh Degrees O Radians sinh 4 5 6 1 2 3 - 0 END VOL BACKSPACE DEL CLEAR Submissions Attempts remaining: 3 (0% per attempt) detailed view 0% 0% N- Submit Hint Feedback I give up! Hints: 0% deduction per hint. Hints remaining: 4 Feedback: 0% deduction per feedback. Feedback Submission History All Dare times are displaved in Central Standard Time Red submission dare times indicate late work. Date Time Answer Hints 1 Jul 30, 2020 4:28 PM 41= 1.5 2 Jul 31, 2020 2:05 PM At = 1.6 A 33% Part (b) How many meters does it travel as observed on the Earth? 4 33% Part (C) How many meters is this in the muon's frame?

Answer 1

v = velocity 0.920 c= (a) solution Using formola at = rato sto life at mums' own frame = 1.5 5 = 1.5X10 out life at the Earth's frame T = 11-12 c2 3x108 mis - 6 Art 1,5x10 3.83 X10 (0192) at = 3.8345 = 3.83X10 (b) Distance traveled in Earth frame. d = speed x time d = 0.92% 3x100 3.83810 1057,08 m. -6. second 1 2 - 6 second 6 d = 1057 m [C? Dis temce teaveled in mums' frame. do = speed oito do = 0.92 X 3 X 10 X 1.5X10 6 do 414 m