Answer to Question #294468 in Classical Mechanics for Jly Miyavi

Question

Assuming that you are moving with a constant speed of 0.65c when you passed by a man on

the sidewalk who started looking at his watch. From your observation, it took him 5 seconds to

look at his watch then look up. How much time elapsed in the man’s frame?

Answer 1

Solution

The time elapsed in the man’s frame

Is given by

$t'=\frac{t}{\sqrt{1-\frac{v^2}{c^2}}}$

Putting all values

$t'=\frac{5}{\sqrt{1-\frac{(0.65c)^2}{c^2}}}\\t'=\frac{5}{\sqrt{0.58}}\\t'=\frac{5}{0.76}\\=6.85sec$