Worksheet: Simultaneity

In this worksheet, we will practice using the Lorentz transformation to calculate the inertial reference frame in which two events are observed to occur simultaneously.

Q1:

Two astronomical events are observed from Earth to occur at a time of 0.30 s apart and a distance separation of 2.0×10 m from each other. How fast must a spacecraft travel from the site of one event toward the other to make the events occur at the same time when measured in the frame of reference of the spacecraft?

  • A 1 . 7 × 1 0 m/s
  • B 2 . 5 × 1 0 m/s
  • C 2 . 9 × 1 0 m/s
  • D 2 . 1 × 1 0 m/s
  • E 1 . 4 × 1 0 m/s

Q2:

An observer sees two events 2.50×10 s apart at a separation of 700 m. How fast must a second observer be moving relative to the first to see the two events occur simultaneously?

  • A 0 . 0 1 1 𝑐
  • B 0 . 1 1 0 𝑐
  • C 0 . 2 5 0 𝑐
  • D 0 . 0 1 0 𝑐
  • E 0 . 0 2 5 𝑐

Q3:

Two astronomical events are observed from Earth. The time difference between the observation of the events is 2 s and the observed distance between the events is 2.5×10 m.

Determine the separation Δ𝑆 of the two events.

  • A 4 × 1 0 m2
  • B 6 × 1 0 m2
  • C 3 × 1 0 m2
  • D 6 × 1 0 m2
  • E 2 × 1 0 m2

Determine whether the separation of the two events is space-like or time-like.

  • ATime-like
  • BSpace-like

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