Lorentz Transformation and position of the object

[Blue Kangaroo]

Homework Statement

Reference frame S' moves at speed v=0.94c in the +x direction with respect to reference frame S. The origins of S and S' overlap at t=t′=0. An object is stationary in S' at position x′ = 140 m .

Part B
What is the position of the object in S when the clock in S reads 1.3 μs according to the Lorentz transformation equations?

Homework Equations

x=γ(x'+vt')

The Attempt at a Solution

I got part A, the Galilean transformation, easily enough. That came out to be 506.6 m. I've been getting the Lorentz transformation wrong and am thinking I'm missing something simple.

I used γ=1/√(1-v^2/c^2) and obtained γ=2.93. I then multiplied this by the Galilean transformation and got ~1485, but Mastering Physics is saying no.

 

[kuruman]

HI Blue Kangaroo and welcome to PF


You are missing a relevant equation involving the time transformation.

You just can't multiply γ "by the Galilean transformation" (whatever that means) and expect to get a sensible answer.

 

[Blue Kangaroo]

My line of thinking was since part A asked for the Galilean transformation (given by x=x'+vt') that that would go directly into the x=γ(x'+vt') equation.

So do I then need to use t=γ(t'+vx'/c^2) and then plug that t into x=γ(x'+vt') to get my final answer?

 

[kuruman]

So do I then need to use t=γ(t'+vx'/c^2) and then plug that t into x=γ(x'+vt') to get my final answer?

Yes, you will get a system of two equations and two unknowns, the position in S that the problem asks you to find and time t' that the problem doesn't ask you to find.