A subatomic particle muon travels at constant velocity 0.9c and lives 1.2us as measured in the muon's frame of reference. How long will the muon lives when measured by an observer on earth?

Q: What must be the speed of an electron for its relativistic kinetic energy to be equal to its rest…

A: The relativistic kinetic energy (KE) of the electron is equal to the rest energy (E).

Q: A spaceship is observed from the Earth to be moving toward a star at a speed of 0.80 c. If the…

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Q: The origins of two frames coincide at t = t' = 0 and the relative speed is 0.975c. Two…

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Q: What is the speed of an electron having the same momentum with a proton having speed 0.005c? (Just…

A: Given data: Speed of proton is, v=0.005c.

Q: An observer in reference frame S′ observes that a lightning bolt strikes the origin, and 1.0×10−4 s…

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Q: A pion is an unstable particle that has an average lifetime of 2.55 x 10$ s. This is the time…

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Q: A space shuttle passes over the Earth at v = 0.90c speed. If the length of space shuttle observed by…

A: Proper length = L∘=100 m Speed = v = 0.9  Say length observed from earth is L The formula used will…

Q: A spacecraft is moving past Earth at a constant speed v which is 0.90c. The astronaut measures the…

A: The time interval ∆t that the observer on Earth measures between the ticks at the astronaut’s clock…

Q: The origins of two frames coincide at t = t' 0 and the relative speed is 0.991c. Two micrometeorites…

A: t=277μS x=83500 m

Q: Observers in reference frame S see an explosion located at x1= 480 m. Asecond explosion occurs 5μs…

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Q: A spacecraft is measured to be 250.00 m long while it is at rest with respect to earth-based…

A: GivenLength of spaceship at rest with respect to observer, Lo=250 mSpeed of spaceship, v=0.8 c

Q: Our spacecraft is passing the Earth at a speed of 0.9c. Then after traveling for 10 years, we make a…

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Q: An observer on the earth sees a spaceship approaching at 0.52c. The ship then launches an…

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Q: A particle is traveling through the Earth’s atmosphere at a speed of 0.750c . To an Earth-bound…

A: Given:  Lo = 2.5 km  v = 0.750 c

Q: A spaceship passes you at a speed of 0.90c. You find the length of the ship in your frame to be 50.0…

A: Given: The speed of spaceship is v=0.90 c Let L0 be the proper length of spaceship. The apparent…

Q: A rod lies parallel to the x axis of reference frame S, moving along this axis at a speed of 0.630c.…

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Q: How far from the earth would you be able to travel in a lifetime of 82 years if you were able to…

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Q: A small meteor, moving through the Solar at a speed of 0.70 c relative to the Earth, has a mass of…

A: Given data:  Speed (V) = 0.70 c Mass (m) = 10.2 kg c = 3×108 m/s

Q: How far from the earth would you be able to travel in a lifetime of 75 years if you were able to…

A: Given:lifetime, ∆t0 = 75 yrsspeed, v = 0.62 c

Q: An observer in reference frame S claims that two events occur simultaneously. As this observer sees…

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Q: A supertrain of proper length 100 m travels at a speed of 0.95c as it passes through a tunnel having…

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Q: The origins of two frames coincide at t = t' 0 and the relative speed is 0.993c. Two micrometeorites…

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Q: While flying past a space station at 0.500c, and at precisely 6.00 seconds before arriving at the…

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Q: In the earth’s rest frame, two protons are moving away from each other at equal speed. In the frame…

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Q: The origins of two frames coincide at t = t' = 0 and the relative speed is 0.956c. Two…

A: If the relative speed between S and S' frame is v then the Lorentz transformation gives the…

Q: A spaceship whose rest length is 350 m has a speed of 0.82c with respect to a certain reference…

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Q: Suppose a cosmic ray colliding with a nucleus in the Earth’s upper atmosphere produces a muon that…

A: Speed of light, c = 3×108 m/sVelocity of muon, v = 0.95cTime period, ∆t0 = 1.52×10-6 s β = vcβ =…

Q: A person on earth notices a rocket approaching from the right at a speed of 0.79c and another rocket…

A: Given  V1 = 0.79c  moving  from  right  to  left  . (w.r.t observer at earth)  V2 = 0.55 c    moving…

Q: A cube of steel has a volume of 1.00 cm3 and mass 8.00 g when at rest on the Earth. If this cube is…

A: It is given that,

Q: A particle moves along the x' axis of frame S' with velocity 0.33c. Frame S' moves with velocity…

A: Given data A particle moves along the x axis of frame s with velocity 0.33c Frame s moves with…

Q: A spacecraft is measured to be 250.00 m long while it is at rest with respect to an earth-based…

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Q: A ground observer made a measurement on a wooden box and the length was found to be 2.3 m. At what…

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Q: How far from the earth would you be able to travel in a lifetime of 81 years if you were able to…

A: Given, Life-time measured in the earth's frame t0 = 81 years. speed (v) =0.82 c where "c" = speed of…

Q: In the lab frame, two protons are moving away from each other at equal speed. In the rest frame of…

A: Let us assume that the earth's rest frame is S, Proton 1's frame is S'. The velocity of Proton 1…

Q: The origins of two frames coincide at t = t' = 0 and the relative speed is 0.991c. Two…

A: a) To find the spatial coordinate of collision for an observer in frame s by Lorentz transformation…

Q: A muon formed high in the Earth's atmosphere travels at a speed 0.870 c for a distance of 4.00 km…

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Q: As measured from the Earth, a spacecraft is moving at speed 0.80 c when it releases a probe at speed…

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Q: A muon travels 60 km through the atmosphere at a speed of 0.9997c. According to the muon, how thick…

A: Given data The initial length is Lo=60 km The speed of muon is v=0.9997c The thickness of the…

Q: The measured mean lifetime of an elementary particle when it is at rest in the lab is measured to be…

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Q: A spaceship, 180 m long as seen on board, moved by the earth at 0.980c. What is it's length in m as…

A: Given data: Original Length (L0) = 180 m Speed (v) = 0.980 c Required: The length of spaceship…

Q: The muon is an unstable particle that spontaneously decays into an electron and two neutrinos. In a…

A: a) The equation to determine the life time of the moving muon is,

Q: A spaceship, 200 m long as seen on board, moves by the Earth at 0.970c . What is its length as…

A: The given values are,

Proper Length

The theory of special relativity explains the connection between space and time to objects that move in a straight line at a constant speed. The objects move at the speed of light. When an object approaches light speed, its mass is endless and cannot move faster than light. The most crucial postulate of Einstein's special relativity is that the laws of nature do not change in each frame of reference.