Chapter 26, Problem 3MCQ

To determine

The proper time interval of the rocket ship adventure.

To determine

Calculation:

To the captain’s frame:

The flashlight flash as measured by the captain can be found

$\Delta t_o=1\times \sqrt{1-\frac{{\left(0.5c\right)}^2}{c^2}}$

$\Delta t_o=0.87\text{ s}$

To the space dock frame:

Suppose if the flashlight is flashes in the space dock and the flashes are recorded by the space dock personal is the proper value and is 1 s

The flashlight flash as measured by the captain is the time dilation value and its value is

$\Delta t=\frac{1}{\sqrt{1-\frac{{\left(0.5c\right)}^2}{c^2}}}$

$\Delta t=1.154$

Analysis of options:

Option a: 1.15 s:

This is not the right answer.

This gives the time dilation value relative to the space dock. So, it is wrong.

Option b: Every 1.00 s:

Hence, it is the wrong answer.

This is measured by the space dock personal and it would be the proper time if the event was held in the space dock. But in our problem statement, it is being held in the rocket. So, it is wrong.

Option c: 0.87 s.:

It is the correct answer.

This is the proper time interval, as calculated above. It is measured by the captain of the rocket the flash light has been flashed from the rocket only. Hence, it is the correct answer.

Option d: 0.13 s:

The proper time and the time interval measured from another reference differ by a factor $\sqrt{1-\frac{v^2}{c^2}}$. The above value does not hold this. Hence, it is the wrong answer.