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An astronaut is standing in a spacecraft parallel to its direction of motion. An observer on the earth finds that the spacecraft speed is 0.60c and the astronaut is 1.3 m tall. What is the astronaut’s height as measured in the spacecraft?

An astronaut is standing in a spacecraft parallel to its direction of motion. An observer on the earth finds that the spacecraft speed is 0.60c and the astronaut is 1.3 m tall. What is the astronaut’s height as measured in the spacecraft?

Grade:12th pass

1 Answers

Avishek Bhagat
askIITians Faculty 71 Points
2 years ago
Dear Student,
according to the problem,

An observer in the same spacecraft, at rest relative to the astronaut, measures the proper length, 1.3m, of the astronaut.
If the astronaut were lying perpendicular to the velocity vector of the spacecraft, the observer on earth would also measure his proper length. But with the astronaut parallel to the direction of relative motion,
the observer on earth measures a contracted length. defining parameters and doing the calculation

L= 1.3 c= 1 V = 0.60c

Lo= L/√1-(v/c)2 = 1.625 meters

askIITians Expert
Yuvraj Sing

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