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## Homework Statement

Event A occurs at x

_{A}= 500m. Event B occurs 5 microseconds later at x

_{B}= 1500m. With what speed must an observer move in the positive x direction so that the events occur at the same point in space in the observer's frame?

## Homework Equations

Lorentz transformation equations:

x' = g(x - Vt)

t' = g(t - (Vx)/c

^{2})

g = 1/sqrt(1 - V

^{2}/c

^{2})

## The Attempt at a Solution

I understand conceptually that, as the observer approaches c, the distance between the two events will contract and the time will "slow down", but I'm unsure how to find these values. Is the V value in the above equations simply the distance divided by time when the events are observed at rest? If so, solving for x' leads to a value of 0. Any help would be greatly appreciated.