Question

If you're in a spaceship traveling at 0.80 c and your trainer on Earth says you must do 90 minutes of exercise every day, how much time, according to a timer on the space vehicle, should you be active to meet your physical activity requirement?

a) 37.5 minutes
b) 45 minutes
c) 52.5 minutes
d) 60 minutes

Answer 1

To calculate the exercise time from the perspective of an astronaut in a spaceship traveling at 0.80 c, we can use the formula for time dilation. Plugging in the values, the astronaut should be active for 45 minutes.

Step-by-step explanation:

To calculate the time for the exercise from the perspective of the astronaut in the spaceship, we need to account for time dilation. Time dilation occurs because objects moving at relativistic velocities experience time differently compared to objects at rest. The formula for time dilation is: t' = t / sqrt(1 - (v^2 / c^2)), where t' is the time dilation, t is the proper time (time on Earth), v is the velocity of the spaceship, and c is the speed of light.

In this case, the velocity of the spaceship is 0.80 c. Plugging the values into the formula, we get: t' = 90 / sqrt(1 - (0.80^2)). Using a calculator, we find that t' is approximately 45 minutes. Therefore, the correct answer is 45 minutes (b).