Two events occur 100 m apart with an intervening time interval of 0.60$\mu$s. The speed of a reference frame in which they occur at the same coordinate is:
A) 0
B) 0.25c
C) 0.56c
D) 1.1c
E) 1.8c

Question

Quizplus · Accepted Answer

We can use the Lorentz transformation equation to solve for the velocity of the reference frame in which the two events occur at the same coordinate:

Δx' = γ(Δx - vΔt)

where:
Δx = distance between the two events = 100 m
Δt = time interval between the two events = 0.60 μs
Δx' = 0 (since the two events occur at the same coordinate in the reference frame we are solving for)
γ = 1/√(1-v²/c²)

Solving for v, we get:

0 = γ(100 - v(0.60×10^-6))
0 = γ(100) - γv(0.60×10^-6)
γv = γ(100)/(0.60×10^-6)
v = c²Δt/Δx = 0.56c

Therefore, the correct answer is C - 0.56c.

Two Events Occur 100 M Apart with an Intervening Time μ\muμ

Two Events Occur 100 M Apart with an Intervening Time $\mu$