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24.10 Lorentz Transformation: Examples
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Module 24: Lorentz Transformation: Examples - Problem 5

A spaceship, whose rest length is 1,560 feet flies by Earth at v=513cv=\frac{5}{13}c. As it does, two firecrackers go off-one at the front of the ship and one at the rear. According to those on the ship, the firecrackers go off at the same moment. (Use the approximation that c=1foot/nsc=1 \,\textrm{foot}/\textrm{ns} and round any answers to the nearest foot, as necessary.)

  1. 1. Question

    According to you, at rest on Earth, how far apart did the firecrackers explode?

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  2. 2. Question

    According to you, what is the length of the spaceship?

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  3. 3. Question

    Now imagine that you have an identical ship sitting right next to you, at rest. You and a friend simultaneously tap the tip and the tail of the stationary ship (simultaneous from the perspective of you and your friend). How far apart do observers on the moving ship claim that the two taps take place? That is, according to observers on the moving ship, how far apart in space are the two events of you tapping the stationary ship and your friend tapping the stationary ship.

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  4. 4. Question

    Observers on the moving ship measure the length of the stationary ship as they zip by. What do they find?

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