Measuring an Event — Question 10

Question 10

A local crossing and its later visual report are distinct events

In one laboratory, two markers follow $x_1=100\,\mathrm m+0.40ct$ and $x_2=700\,\mathrm m-0.20ct$. Their crossing emits a flash detected at the origin. Use $c=3.00\times10^8\,\mathrm{m/s}$ and Einstein-synchronized laboratory clocks.

1. Find the crossing event.

2. Find the flash reception time and the delay between crossing and report.

Question 10 - Solution

A local crossing and its later visual report are distinct events

(a) Method and calculation

$$100+0.40ct_E=700-0.20ct_E\quad\Rightarrow\quad ct_E=1000\,\mathrm m.$$$$\boxed{t_E=3.333\,\mu\mathrm s},\qquad\boxed{x_E=500\,\mathrm m}.$$

(b) Interpretation and further calculation

$$t_R=t_E+x_E/c=\boxed{5.000\,\mu\mathrm s}.$$$$\boxed{t_R-t_E=1.667\,\mu\mathrm s}.$$

Physical check

All observers agree that the two markers meet locally, even though their coordinate assignments and report times may differ.