A stationary unstable particle has an average lifetime of 3 [m] in its rest frame. If its average lifetime as measured by a rocket frame moving at a speed of B relative to the particle is 5 [m] what is 3?
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![A stationary unstable particle has an average
lifetime of 3 [m] in its rest frame. If its average lifetime as
measured by a rocket frame moving at a speed of B relative to
the particle is 5 [m] what is 3?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5f73f2f-aceb-4fab-9cfc-9170b94659da%2F42d64be4-c798-4078-8f16-c1c7f96de468%2F5eozw38_processed.png&w=3840&q=75)

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- A muon is determined to live for 2.2E[-6]s in the muon's rest reference frame. If a muon is traveling near the speed of light relative to an observer, the observer will measure the duration of the muon's life to be ...An electron moving at 0.80c relative to the Earth reference frame travels the 100m length of a building (as measured in the Earth reference frame). What is the length of the building according to an observer moving along with the electron?12. (a) A particle is traveling through the Earth's atmosphere at a speed of 0.750c. To an earth bound observer, the distance it travels is 2.5km. How far does the particle travel in the particle's frame of reference? (b) Calculate the momentum of an electron traveling at a speed 0.985c? The rest mass of the electron is 9.11 X 10-31 kg.
- An elementary particle produced in a laboratory experiment travels 0.230 mm through the lab at a relative speed of 0.960c before it decays (becomes another particle). (a) What is the proper lifetime of the particle? (b) What is the distance the particle travels as measured from its rest frame?A spaceship that has a rest length of 200 m passes by earth at a speed in which only (1/4) x 10-6 s is required for it to pass by a given point as measured by clocks on earth. How fast is it moving and at what length (according to observers on earth)?Consider a cosmic ray colliding with a nucleus in the Earth's upper atmosphere that produces a muon which has a velocity v = 0.916c. The muon then travels at constant velocity and lives 1.52 µs as measured in the muon's frame of reference. (You can imagine this as the muon's internal clock.) (a) How far (in km) does the muon in travel according to an Earth-bound observer? (b) How far (in km) does it travel as viewed by an observer moving with it? Base your calculation on its velocity relative to the Earth and the time it lives (proper time).
- A rocket measures 100 m long in its own frame (S') and is travelling at 0.995c relative to a frame S. At the tail of the rocket, a laser sends out a pulse of light which is reflected by a mirror at the nose of the rocket. (a) At what time after emission, measured in S', does the light pulse arrive back at the tail of the rocket? (b) At what time after emission, measured in S, does the light pulse arrive back at the tail of the rocket? (c) What is the spatial distance, measured in S, between the emis- sion of the pulse and its arrival back at the tail of the rocket? (d) At what time after emission, measured in S, does the light pulse hit the mirror? (e) What is the spatial distance, measured in S, between the emis- sion of the pulse and its hitting the mirror? (f) Can you conclude from your answers that the light pulse travelled at a different speed, as seen in S, on its way to the mirror than on the way back? If not, explain your resultsAn unstable high-energy particle is created in the laboratory, and it moves at a speed of 0.992c. Relative to a stationary reference frame fixed to the laboratory, the particle travels a distance of 1.05 × 10-3 m before disintegrating. What is (a) the proper distance and (b) the distance measured by a hypothetical person traveling with the particle? Determine the particle's (c) proper lifetime and (d) its dilated lifetime. (a) Number Units (b) Number Units (c) Number Units (d) Number Units