Space cruisers A and B are moving parallel to the positive direction of an x axis. Cruiser A is faster, with a relative speed of v = 0.900c, and has a proper length of L = 200 m. According to the pilot of A, at the instant (t = 0) the tails of the cruisers are aligned, the noses are also. According to the pilot of B, how much later are the noses aligned?

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: As the drawing shows, a carpenter on a space station has constructed a 30.0° ramp. A rocket moves…

A: v = 0.854cwhere c is the speed of lightθ = 30° Since it is in x-direction, there will be length…

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

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Q: Saturn is 1.43 x 1012 m from the sun. A rocket travels along a line from the sun to Saturn at a…

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Q: A space shuttle passes the Earth at a speed of 0.80c. If the space shuttle is 30 m in length as…

A: Given: The speed of the space shuttle is 0.8c. The length of the space shuttle is 30 m.

Q: Two spaceships approach the Earth from opposite directions. According to a stationary observer on…

A: Given that:- Two spaceships A and B approch the earth from opposite directions.

Q: A spaceship in distress sends out two escape pods in opposite directions. One travels at a speed v1…

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Q: A rod of length 2.0 m is at rest in S’ and is tilted at an angle of 35 degrees with respect to the…

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Q: alculate the interval Δs2 between two events with coordinates (x1 = 55m, y1 = 0m, z1 = 0m, t1 = 1…

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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 supertrain of proper length 94 m travels at a speed of 0.93c as it passes through a tunnel having…

A: The Lorentz transformation is the contraction of length l of any object with respect to the moving…

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: Calculate the interval ∆s2 between two events with coordinates (x1 = 50 m, y1 = 0, z1 = 0, t1 = 1…

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Q: As the drawing shows, a carpenter on a space station has constructed a 30.0° ramp. A rocket moves…

A: Solution: Given: θ1 = angle of ramp constructed on space station = 30.0o     v = speed of rocket…

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

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Q: The proper length of one spaceship is three times that of another. The two spaceships are traveling…

A: Consider The proper length of slower spaceship is "L" The proper length of faster spaceship "3L"The…

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 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: Inertial frame S' moves at a speed of 0.60c with respect toframe S. Further, x = x' = 0 at t = t' =…

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Q: Frame S' has a speed v = 0.6c relative to S in x direction which is parallel to x'. The clocks on S…

A: Given : Speed of S' with respect to S, v = 0.6c The clocks on S and S' are adjusted so that t= t'= 0…

Q: An astronaut travels in a rocket along the +x direction with a velocity of 0.50c relative to the…

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Q: A rocket cruises past a laboratory at 0.400 x 10° m/s in the positive I-direction just as a proton…

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

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Q: A base on Planet X fires a missile toward an oncoming space fighter. The missile’s speed according…

A: The expression for velocity of an object is, u'=u-v1-uvc2

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: Calculate the interval ∆s^2 between two events with coordinates (x1 = 50 m, y1 = 0, z1 = 0, t1 = 1…

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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: An alien spacecraft moving with the speed of 0.30c with respect to Earth, fires photon torpedoes…

A: Given: Alien spacecraft speed, v = 0.30c Speed of the photon torpedo with respect to the spaceship,…

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

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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 rocket launched outward from Earth has a speed of 0.38c relative to the Earth. The rocket is…

A: The speed of the meteor as observed from earth is     0.435967c  m/s.

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: The positive muon (µ), an unstable particle, lives on average 2.20 x 10 reference) before decaying.…

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Q: According to observer O, a blue flash occurs at ?1 = 10.4m when ?1 = 0.124µs and a red flash occurs…

A: Given : x1 = 10.4 m t1 = 0.124µs = 0.124 x 10-6 s x2 = 23.6 m t2 = 0.138µs = 0.138 x 10-6 s

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

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Q: A tracking station on Earth observes a rocket move away at 0.370c. This rocket is designed to launch…

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Q: Calculate the interval ∆s2 between two events with coordinates ( x1 = 50 m, y1 = 0, z1 = 0, t1 = 1…

A: Einstein with his special theory of relativity brought in an entirely new understanding of the world…

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.