The Lorentz Transformation and Velocity Addition · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

When speed mixes space and time

Science · Quantum & Modern Physics · ages 19-20
Name ______________________   Date ____________
  1. Two ships pass at ever higher relative speed. What happens to gamma?

    • It stays exactly 1
    • It shrinks toward zero
    • It grows without bound
  2. Frame S prime drifts past frame S at speed v along x. Which pair converts an event between them?

    • x alone, since time runs the same
    • x prime and t prime through gamma, v, and c
    • v alone, since positions match
  3. Two bulbs at the ends of a 26 m car flash together for a trackside watcher while the car passes at half light speed. What does the seated passenger see?

    • The flashes at different times
    • The flashes together, like the watcher
    • No flashes at all
  4. A ship racing Earthward at half light speed shines a laser ahead. At what speed does the light approach Earth?

    • 1.5 c
    • 0.5 c
    • Still c
  5. A ship at 0.5 c fires a canister forward at 0.75 c. Type the speed Earth sees, in units of c.

    Answer: ______________

  6. Two cars approach at motorway speeds. Why does the relativistic rule agree with ordinary addition?

    • Gamma is infinite at low speeds
    • The fraction bottom is nearly 1 at low speeds
    • Light speed is zero for slow objects
  7. Two ticks happen at the same spot aboard a passing ship. How do you get the dilated time on your clock?

    • Just add the ship speed to the tick count
    • Transform the pair with the Lorentz time line and read off the stretched gap
    • Measure the ship length instead
  8. Adding 0.5 c and 0.75 c in the same direction can reach 1.25 c.

    Circle one:   True   False

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Answer key

For grown-ups. Fold this page away before handing over the rest.

When speed mixes space and time W1-mt_uG3_gArw19-s1

  1. It grows without bound · Gamma is 1 over a shrinking root, so it climbs as v nears c.
  2. x prime and t prime through gamma, v, and c · The Lorentz change mixes x with t through gamma, v, and c.
  3. The flashes at different times · Simultaneity bends: the passenger moves toward one flash and away from the other.
  4. Still c · Light leaves at c and arrives at c, whatever the ship does.
  5. 0.909 · The fraction gives 1.25 over 1.375, which is 0.909 c.
  6. The fraction bottom is nearly 1 at low speeds · At low speeds v u prime over c squared is tiny, so the fraction is nearly plain addition.
  7. Transform the pair with the Lorentz time line and read off the stretched gap · Same-spot ticks fed through the Lorentz time line come out stretched: that is dilation.
  8. False · The relativistic sum is 0.909 c, always below light speed.
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