Question

Your job is to synchronize the clocks in a reference frame. You are going to do so by flashing a light at the origin at $\mathrm{t}=0\mathrm{s}$. To what time should the clock at $(\mathrm{x},\mathrm{y},\mathrm{z})=(30\mathrm{m},40\mathrm{m},0\mathrm{m})$ be preset?

Short answer

The time is$166.6\mathrm{ns}.$

Step-by-step solution

Given information

We have given,

$(\mathrm{x},\mathrm{y},\mathrm{z})=(30\mathrm{m},40\mathrm{m},0\mathrm{m})$

We have to find the time in the clock at that position.

Simplify

The distance will travel,

$$\begin{gathered} \mathrm{R}=\sqrt{{\mathrm{x}}^2+{\mathrm{y}}^2+{\mathrm{z}}^2} \\ \mathrm{R}=\sqrt{{\left(30\right)}^2+{\left(40\right)}^2+0} \\ \mathrm{R}=\sqrt{900+1600} \\ \mathrm{R}=\sqrt{2500} \\ \mathrm{R}=50\mathrm{m}/\mathrm{s} \end{gathered}$$

Since, the speed will speed of the light c.

Then time taken for the light to travel,

$$\begin{gathered} \mathrm{t}=\frac{\mathrm{R}}{\mathrm{V}}=\frac{50\mathrm{m}/\mathrm{s}}{3\times {10}^8\mathrm{m}/\mathrm{s}} \\ \mathrm{t}=166.6\mathrm{ns} \end{gathered}$$