Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon...
Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon that has speed v = 0.74c. The muon then travels at constant speed and lives 1.525 μs as measured in the muon's frame of reference. (You can imagine this as the muon's internal clock.) Please answer B
A) How many kilometers does the muon travel according to an Earth-bound observer?
0.503 is the answer to A
B) How many kilometers of the Earth pass by as viewed by an observer moving with the muon? Base your calculation on its speed relative to the Earth and its lifetime (proper time).
Homework Answers
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Suppose a cosmic ray colliding with a nucleus in the Earth's
upper atmosphere produces a muon...
Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon...
Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon that has speed v= 0.83c. 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 v=0.83c t=1.5 us (a) How long does the muon live in seconds) as observed on the Earth? b) How many meters does it travel as observed on the Earth?...
Suppose a muon produced as a result of a cosmic ray colliding with a nucleus in...
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 ps 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...
Suppose a muon produced as a result of a cosmic ray colliding with a nucleus in...
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...
(15%) Problem 8: Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere...
(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...
A high energy cosmic ray hits the upper atmosphere, 10km above the earth, and produces a...
A high energy cosmic ray hits the upper atmosphere, 10km above the earth, and produces a muon travelling and 0.99c. (a) How long does it take the muon to hit the earth's surface in the earth's reference frame? (b) How long does it take to hit the surface in the muon's reference frame? (c) If the mean lifetime of a muon is 2.2us what is the chance that it will reach the earth's surface?
A high energy cosmic ray hits the upper atmosphere, 10km above the earth, and produces a...
A high energy cosmic ray hits the upper atmosphere, 10km above the earth, and produces a muon travelling and 0.99c. (a) How long does it take the muon to hit the earth's surface in the earth's reference frame? (b) How long does it take to hit the surface in the muon's reference frame? (c) If the mean lifetime of a muon is 2.2us what is the chance that it will reach the earth's surface?
A muon is produced by a collision between a cosmic ray and an oxygen nucleus in...
A muon is produced by a collision between a cosmic ray and an oxygen nucleus in the upper atmosphere at an altitude of 50 kml. It travels vertically downward to the surface of the Earth where it arrives with a total energy of 232 MeV|. The rest energy of a muon is 105.7 MeV|. What is the kinetic energy of a muon at the surface? 1.26 times 10^2 MeV What is the velocity of a muon at the surface? (Give...
A cosmic ray travels 60 km through the earth's atmosphere in 410 μs , as measured...
A cosmic ray travels 60 km through the earth's atmosphere in 410 μs , as measured by experimenters on the ground. Please show work.
One of the most impressive experimental confirmations of Time Dilation involves muons. Muons are unstable elementary...
One of the most impressive experimental confirmations of Time Dilation involves muons. Muons are unstable elementary particles with a lifetime of 2.2 μμs. They are naturally produced in collisions between cosmic radiation and atoms in our upper atmosphere (~3000m above the Earth's surface). A muon travels at 0.98c. In a reference frame that is attached to the moving muon (the muon's reference frame), how far can the muon travel before it decays (recall that v = d/t)? For an observer...
A cosmic ray travels 58 km through the Earth's atmosphere in 400 microseconds, as measured by...
A cosmic ray travels 58 km through the Earth's atmosphere in 400 microseconds, as measured by experimenters on the ground. How far does the cosmic ray travel in its own frame of reference? km
Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon that has speed v= 0.83c. 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 v=0.83c t=1.5 us (a) How long does the muon live in seconds) as observed on the Earth? b) How many meters does it travel as observed on the Earth?...
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 ps 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...
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...
(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...
A high energy cosmic ray hits the upper atmosphere, 10km above the earth, and produces a muon travelling and 0.99c. (a) How long does it take the muon to hit the earth's surface in the earth's reference frame? (b) How long does it take to hit the surface in the muon's reference frame? (c) If the mean lifetime of a muon is 2.2us what is the chance that it will reach the earth's surface?
A high energy cosmic ray hits the upper atmosphere, 10km above the earth, and produces a muon travelling and 0.99c. (a) How long does it take the muon to hit the earth's surface in the earth's reference frame? (b) How long does it take to hit the surface in the muon's reference frame? (c) If the mean lifetime of a muon is 2.2us what is the chance that it will reach the earth's surface?
A muon is produced by a collision between a cosmic ray and an oxygen nucleus in the upper atmosphere at an altitude of 50 kml. It travels vertically downward to the surface of the Earth where it arrives with a total energy of 232 MeV|. The rest energy of a muon is 105.7 MeV|. What is the kinetic energy of a muon at the surface? 1.26 times 10^2 MeV What is the velocity of a muon at the surface? (Give...
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