A pion is created in the higher reaches of Earth’s atmosphere when an incoming high-energy cosmic-ray particle collides with an atomic nucleus. A pion so formed descends toward Earth with a speed of 0.99c. In a reference frame in which they are at rest, pions decay with an average life of 26 ns. As measured in a frame fixed with respect to Earth, how far (on the average) will such a pion move through the atmosphere before it decays?

Q: A neutral K meson at rest decays into two t mesons, which travel in opposite directions along the x…

A:

Q: An astronaut at rest on Earth has a heart rate of 70. beats/min. When the astronaut is traveling in…

A: The formula to calculate the heart beat rate is,

Q: The elementary particle called a muon is unstable and decays in about 2.20μs, as observed in its…

A:

Q: A neutral -meson is a particle that can be created by accelerator beams. If one such particle lives…

A:

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

A:

Q: Two neutron stars are separated by a distance of 1.0 x 1011 m. They each have a mass o are initially…

A: Given:- The separation distance between the two neutron stars r= 1.0 x 1011 m  They have a mass m =…

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: An astronaut travels away from the Earth at a speed of 0.95c and sends a light signal back to the…

A: In the given question, Speed of the astronaut = 0.95c It travels away from earth. The astronaut…

Q: A subatomic particle muon travels at constant velocity 0.9c and lives 1.2us as measured in the…

A:

Q: Otávio and Diana are at rest in the frame S', which moves at 0.600c in

A: Yes

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

A:

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

A:

Q: A spacecraft with the shape of a sphere of diameter D moves past an observer on Earth with a speed…

A: The length of the object contacted in the direction of its motion.The contracted length is

Q: kg, An unstable particle at rest spontaneously breaks into two fragments of unequal mass. The mass…

A: Given Data Mass of the first fragment is m1=2.80×10-28 kg Mass of the other fragment is…

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: A spacecraft with a proper length of 250 m passes by an observer on the Earth. According to this…

A: proper length (Lo) = 250 m Let the speed of spacecraft = v time taken to pass a point as observed by…

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

A: We have two inertial frames of references as S and S' with coordinates (x, y, z, t) and (x', y', z',…

Q: A supertrain of proper length 1.00 X 102 m travels at a speed of 0.95c as it passes through a tunnel…

A: Formula to calculate the contacted length of the train measured by the track side observer is,

Q: Two neutron stars are separated by a distance of 1.0 * 10^10 m. They each have a mass of 1.0 * 10^30…

A:

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

A:

Q: A spacecraft with a proper length of Lp passes by an observer on the Earth. According to this…

A: It is known that when an object moves in high speed with respect to an observer then its length…

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

A:

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

A:

Q: If an object at rest in a given frame has no potential energy, then it has a)a rest energy of mc2…

A: Potential energy is the energy of an object due to its position with respect to other objects,…

Q: An astronaut exercising on a treadmill maintains a pulse rate of 150 per minute. If he exercises for…

A:

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

A:

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: A space cowboy wants to eject from his spacecraft 100,000 km after passing a space buoy, as seen by…

A: Given: The distance covered is 100000 km. The speed is 0.300 c.

Q: 2.2. A rod of mass m = 1 kg flies with constant velocity past a mark which is stationary in the K…

A:

Q: Two identical particles P and Q of rest mass m,, are moving with velocities 5c 2c and 19 in…

A:

Q: What will be the mean lifetime of a muon as measured in the laboratory if it is traveling at v=0.1c…

A:

Q: A person on Earth observes two rocket ships moving directly toward each other and colliding as shown…

A: Relative velocity question, solution given in image

Q: e t = 0 in the Earth frame, the Earth observer determines that rocket A, travelling to the right at…

A: We draw a figure according to the given data in the question  here l= 4.2 x 108 m   [ Given ]

Q: An armada of spaceships that is 1.00 ly long (as measured in its rest frame) moves with speed 0.800c…

A:

Q: The positive muon (?+), an unstable particle, lives on average 2.20?10−16 ? (measured in its own…

A: Given: A positivive mu+ Time ∆to = 2.20 × 10-16 s u = 0.900c To determine: Average lifetime and…

Q: A particle is traveling through the Earth’s atmosphere at a speed of 0.119c . To an Earth-bound…

A:

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.