The Power of Simultaneity: Tips for Taking the First Step

[ChrisWM]

Homework Statement

An observer in an inertial reference frame experiences two events simultaneously at positions x1 = 1.51 km and x2 = 9.89 km . A second observer in an inertial reference frame moving with𝛽=0.783 in the +x direction relative to the first observer, experiences the same two events. What (a) distance between the events and (b) time interval between the events does the second observer measure? (c) What does each observer measure for the spacetime invariant, Δ𝑠^2 ? (Hint for (c): invariant)

Relevant Equations

x'=(x-vt)/sqrt(1-v^2/c^2)

What is my first step here? I'm not sure of where to start?

 

[PeroK]

Homework Statement:: An observer in an inertial reference frame experiences two events simultaneously at positions x1 = 1.51 km and x2 = 9.89 km . A second observer in an inertial reference frame moving with𝛽=0.783 in the +x direction relative to the first observer, experiences the same two events. What (a) distance between the events and (b) time interval between the events does the second observer measure? (c) What does each observer measure for the spacetime invariant, Δ𝑠^2 ? (Hint for (c): invariant)
Relevant Equations:: x'=(x-vt)/sqrt(1-v^2/c^2)

What is my first step here? I'm not sure of where to start?

What about the Lorentz Transformation?