Lorentz transformation: System S' has a velocity u = +0.45c relative to system S, as shown in the figure. The clocks of S and S' are synchronized at t = t' = 0 when the origins O and O' coincide. An event is observed in both systems. The event takes place at x = 600 m and at time t = 1.9 μs, as measured by an observer in S. What is the x'-coordinate of the event, measured by an observer in S'?
A) 380 m
B) 340 m
C) 360 m
D) 350 m
E) 310 m

Question

Lorentz transformation: System S' has a velocity u = +0.45c relative to system S, as shown in the figure. The clocks of S and S' are synchronized at t = t' = 0 when the origins O and O' coincide. An event is observed in both systems. The event takes place at x = 600 m and at time t = 1.9 μs, as measured by an observer in S. What is the x'-coordinate of the event, measured by an observer in S'? 
A) 380 m 
B) 340 m 
C) 360 m 
D) 350 m 
E) 310 m

Quizplus · Accepted Answer

Using the Lorentz transformation formula for the x coordinate:

$x'=\gamma(x-ut)$

where $\gamma=\frac{1}{\sqrt{1-\frac{u^2}{c^2}}}$ is the Lorentz factor.

Plugging in the given values, we get:

$x'=\gamma(x-ut)=\frac{1}{\sqrt{1-\frac{(0.45c)^2}{c^2}}}(600	ext{ m}-0.45c	imes1.9	ext{ μs})\approx 380	ext{ m}$

Therefore, the x'-coordinate of the event, measured by an observer in S', is 380 m.

Lorentz Transformation: System S' Has a Velocity U = +0