Question
A spaceship, 200 m long as seen on board, moves by the
Earth at 0.970c . What is its length as measured by an
Earth-bound observer?
Final Answer
Solution video
OpenStax College Physics for AP® Courses, Chapter 28, Problem 12 (Problems & Exercises)
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Video Transcript
This is College Physics Answers with Shaun Dychko. A spaceship is measured to be 200 meters long according to a person that's on the ship this is going to be labeled L naught— the proper length— because the person on the ship is at rest with respect to the two end points that are being measured between so the spaceship has one end point here at the tip and another end point at the booster rocket I guess and then the person on the ship is at rest with respect to those end points and so the length they measure is the proper length. The ship is zipping past the Earth at a speed of 0.970c and the question is what length will an Earth-based observer measure for this ship? So the ship is zipping past the Earth at a speed v. Okay! This is going to be a shorter length, it's going to be a contracted length according to the Earth-based observer and that length will be the proper length times the square root of 1 minus v squared over c squared. You might also see this as L equals L naught divided by γ and if you expand γ and replace it, you'll end up with this formula here. So we have 200 meters times the square root of 1 minus 0.970c squared divided by c squared and this is 48.6 meters.