The relativity of time: Time dilation

[MrDMD83]

Homework Statement

Suppose that you are traveling on board a spacecraft that is moving with respect to the Earth at a speed of 0.925c. You are breathing at a rate of 10.0 breaths per minute. As monitored on earth, what is your breathing rate in breaths per minute?

Homework Equations

t=t0/(1-v^2/c^2)^1/2

The Attempt at a Solution

t=1/(1-(.925x3e8)^2/(3e8)^2)^1/2

Not really sure where to go from here.

 

[Doc Al]

You are on the right track--don't stop now.

Your breathing is a "clock" like any other. Viewed from the earth, you are a moving clock which is measured to run slowly by a factor given by that equation. Complete the calculation!

Note: Better to write the equation for "time dilation" as:
$$\Delta T = \Delta T_0 \frac{1}{\sqrt{1 - v^2/c^2}}$$

Where $$\Delta T_0$$ is the time it takes you to breath 10 breaths (1 minute, as measured by you) and $$\Delta T$$ is the time (the number of Earth minutes) that Earth measurements say it took you to breath those 10 breaths. Use that Earth time to calculate your breathing rate according to Earth clocks.