Relative to Reference Frame 1, Reference Frame 2 Moves with Speed

question 26

Multiple Choice

Relative to reference frame 1, reference frame 2 moves with speed v in the negative x direction. When the origins of the two frames coincide the clocks in both frames are set to zero. An event occurs at coordinate x₁ and time t₁ as measured in reference frame 1 and at coordinate x₂ and time t₂ as measured in frame 2. If , then the coordinates and times of the event are related by:

• A) x₂ = \(\gamma\)[x₁ - vt₁] and t₂ = \(\gamma\)[t₁ - vx₁ / c²]
• B) x₂ = \(\gamma\)[x₁ - vt₁] and t₂ = \(\gamma\)[t₁ + vx₁ / c²]
• C) x₂ = \(\gamma\)[x₁ + vt₁] and t₂ = \(\gamma\)[t₁ - vx₁ / c²]
• D) x₂ = \(\gamma\)[x₁ + vt₁] and t₂ = \(\gamma\)[t₁ + vx₁ / c²]
• E) none of the above are correct

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Definitions:

Inductive

A reasoning method that entails moving from specific observations to broader generalizations and theories.

Deductive

A logical process where a conclusion follows necessarily from the set of premises, provided the premises are true.

Hasty Generalization

A reasoning error where the conclusion is not supported by enough or impartial evidence.

Blizzard

A severe snowstorm characterized by strong sustained winds of 35 mph or more and lasting for a prolonged period of time, typically three hours or more.