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A spaceship is travelling with a velocity of 0.7c away from a space station. The spaceship ejects a probe with a velocity 0.59c opposite to its own velocity. A person in the space station would see the probe moving at a speed Xc, where the value of X is ________ (up to three decimal places).
Correct answer is '0.185 to 0.189'. Can you explain this answer?
Most Upvoted Answer
A spaceship is travelling with a velocity of 0.7c away from a space st...
Explanation:

  • Velocity of spaceship (v) = 0.7c

  • Velocity of probe ejected from spaceship (u) = -0.59c (opposite direction to spaceship's velocity)

  • We need to find the velocity of the probe as observed by a person in the space station (let's call it w)

  • We can use the relativistic velocity addition formula to find w:



Relativistic velocity addition formula:
w = (u + v)/(1 + uv/c^2)
where c = speed of light

Substituting values:
w = (-0.59c + 0.7c)/(1 - 0.59c*0.7c/c^2)
w = 0.11c/0.5923
w = 0.185c

Therefore, the velocity of the probe as observed by a person in the space station is 0.185c.

Note:
The answer given in the question is a range (0.185 to 0.189c), which is due to the fact that the velocity addition formula involves square roots and rounding off errors may occur.
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A spaceship is travelling with a velocity of 0.7c away from a space station. The spaceship ejects a probe with a velocity 0.59c opposite to its own velocity. A person in the space station would see the probe moving at a speed Xc, where the value of X is ________ (up to three decimal places).Correct answer is '0.185 to 0.189'. Can you explain this answer?
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A spaceship is travelling with a velocity of 0.7c away from a space station. The spaceship ejects a probe with a velocity 0.59c opposite to its own velocity. A person in the space station would see the probe moving at a speed Xc, where the value of X is ________ (up to three decimal places).Correct answer is '0.185 to 0.189'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A spaceship is travelling with a velocity of 0.7c away from a space station. The spaceship ejects a probe with a velocity 0.59c opposite to its own velocity. A person in the space station would see the probe moving at a speed Xc, where the value of X is ________ (up to three decimal places).Correct answer is '0.185 to 0.189'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A spaceship is travelling with a velocity of 0.7c away from a space station. The spaceship ejects a probe with a velocity 0.59c opposite to its own velocity. A person in the space station would see the probe moving at a speed Xc, where the value of X is ________ (up to three decimal places).Correct answer is '0.185 to 0.189'. Can you explain this answer?.
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