An astronaut in a spaceship is listening to his music. Calculate the time it takes to play a 4.00 minute song at 0.1c
Whose watch?
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To calculate the time it takes to play a 4.00 minute song at 0.1c, we need to take into account time dilation, which occurs due to the relativistic effects of traveling at high speeds.
The equation for time dilation is:
t' = t / √(1 - v^2/c^2)
Where:
t' = time as experienced by the astronaut
t = time as measured in the stationary frame (Earth)
v = velocity of the spaceship
c = speed of light
In this case, the velocity of the spaceship is 0.1c. So, v = 0.1c.
Substituting these values into the equation, we get:
t' = 4 / √(1 - (0.1c)^2/c^2)
Simplifying further:
t' = 4 / √(1 - 0.01)
t' = 4 / √(0.99)
t' = 4 / 0.9949874371
t' ≈ 4.02 minutes
Therefore, according to the time dilation effect, it would take approximately 4.02 minutes for the astronaut to play a 4.00 minute song at 0.1c.