Answer to Question #89320 in Mechanics | Relativity for Sridhar

Question

at what speed should backlog be more so that may appear to lose 1 minute in each hour

Answer 1

Amazing question about time!

Imagine that we have a common task that requires exactly 60 minutes to be completed. But you lost a minute and now you have only 59 minutes to complete it. So you can take a ride on a starship moving incredibly fast. Your goal is to move such a high speed so that you could have 60 minutes to complete this task meanwhile back on Earth it would seem to be 59 minutes. What speed should you offer to the captain of the starship to do your homework?

The following equation from Special relativity will help you:

$$t=\frac{t_0}{\sqrt{1-v^2/c^2}},$$

where $t=60\text{ min}$ is time that you'll count cruising on a board, $t_0=59\text{ min}$ is the time on the Earth, $c=3\cdot10^8\text{ m/s}$ is the speed of light. Express the speed $v$:

$$v=c\sqrt{1-\frac{t_0^2}{t^2}}=3\cdot10^8\sqrt{1-\frac{59^2}{60^2}}=54543561\text{ m/s},$$

or about 55000 km/s.