Question

Suppose a muon produced as a result of a cosmic ray colliding with a nucleus in the upper atmosphere has a velocity v = 0.950c. Suppose it travels at constant velocity and lives 2.20 us as measured by an observer who moves with it (this is the time on the muon's internal clock). It can be shown that it lives for 4.87 us as measured by an Earth-bound observer. (a) How long (in us) would the muon have lived as observed on Earth if its velocity was 0.627c? 6.900-6 X What is time dilation? What is the y factor? Can you simplify it by canceling c? MS (b) How far (in m) would it have traveled as observed on Earth? m (c) What distance (in m) is this in the muon's frame? m

Answer 1

And! given That - 0.95c Veloute of muong + propen time & 2045 dialate time 4.87 43. li if a= 0.6270 ta to I-0202 tot diolate time to propey time. 10 to (0.6270)2 C2 tato 2.20 45 |- (0.627) ? 3 2.85 MI eis on obseyred at eau Thi veloute distance time distance velocity a time 0.62 7 x 3 x 108 x 2.88x10-6 uinis 536m In muons frame: distance = 0.627* 310 x 4.20x10 413 m.