An astronaut is traveling in a space vehicle moving at 0.500c relative to the Earth. The astronaut measures her pulse rate at 75.0 beats per minute. Signals generated by the astronaut’s pulse are radioed to the Earth when the vehicle is moving in a direction perpendicular to the line that connects the vehicle with an observer on the Earth. (a) What pulse rate does the Earth-based observer measure? (b) What If? What would be the pulse rate if the speed of the space vehicle were increased to 0.990c?

Q: An astronaut at rest on Earth has a heartbeat rate of 90 beats/min. When the astronaut is traveling…

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Q: A spacecraft is launched from the surface of the Earth with a velocity of 0.600c at an angle of…

A: Given: The velocity v1 = 0.6c, The velocity v2 = 0.7c, Angle of velocity v1 with x axis = 50.0

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: The control panel on a spaceship contains a light that blinks every 2.71 s as observed by an…

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Q: Electromagnetic radiation from a star is observed with an earth-based The star is moving away from…

A: The Doppler effect is the change in the observed frequency of an electromagnetic wave due to…

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: 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: 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: 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: ay from Earth? (b)To what frequency must Earth receivers be tuned to receive the report when the…

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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: The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6…

A: Given, The average lifetime of a pi meson t = 2.6 x 10-8 s.   (a) If the meson moves with a speed of…

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

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Q: The cosmic rays of highest energy are protons that have kinetic energy on the order of 1013 Mev. (a)…

A: Given: Kinetic energy of proton = 1013MeV = 1.6×10-6MJ = 1.6 J Diameter of Galaxy, d = 7.80×104ly

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: The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6…

A: a) The mean life time pf the pi meson with respect to the proper time on the earth is,

Q: A spaceship, moving away from Earth at a speed of 0.900c, reports back by transmitting at a…

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Q: is 0.961c. Two micrometeorites collide at coordinates x = 129 km and t = 192 μs according to an…

A: Given:- The origins of the two frames coincide at t = t' = 0 and the relative speed is 0.961c. Two…

Q: A tuning fork has a frequency of 800 Hz and hence a period of 1.25 × 10 −3 s. If the tuning fork is…

A: The given values are, f=800 HzT=1.25×10-3 sv=0.690c

Q: If two spaceships are heading directly towards each other at 0.800c , at what speed must a canister…

A: Given information: Here v is the speed of each spaceship S1 and S2, and ux’ is the speed of the…

Q: Suppose a space probe moves away from the Earth at a speed 0.350c . It sends a radio wave message…

A: The speed of the space prob, v=0.350 c   The frequency of the source, fs=1.50 GHz

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: A space traveler takes off from Earth and moves at speed 0.9900c toward the star Vega, which is…

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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: Suppose a celestial body is moving away from the Earth at a speed of 0.325c. It emits radio waves…

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Q: Answering an emergency beacon, Captain Jack leaves the Earth on a rescue mission at 0.60c, arriving…

A: Given data: -  The speed at which Captain Jack leaves the earth is v = 0.60c. The arrival time at…

Q: A spaceship travels at 0.750c relative to Earth. If the spaceship fires a small rocket in the…

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

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Q: A Foron cruiser moving directly toward a Reptulian scout ship fires a decoy toward the scout ship.…

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Q: A spaceship carrying a light clock moves at a speed of 0.6c relative to an observer on Earth. If the…

A: Given data The speed of the spaceship is given as v = 0.6c. The time advances by the ship on the…

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

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

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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.