Question

Using the formula for time dilation, Δt_relative = Δt / √(1 - v²/c²), solve the problem below:

On Earth, your strength and conditioning trainer determine you must do 90 minutes of exercise every day. If the vehicle is traveling at 0.80c, 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) 50 minutes
c) 75 minutes
d) 112.5 minutes

Answer 1

To solve this problem, we can use the formula for time dilation. Substituting the given values into the formula, the relative time as measured by the observer on the space vehicle is calculated.

Step-by-step explanation:

To solve this problem, we can use the formula for time dilation, Δt_relative = Δt / √(1 - v²/c²). In this case, the Earth-bound observer measures the time as 90 minutes (Δt). We need to find the relative time (Δt_relative) as measured by the observer on the space vehicle. The velocity of the vehicle is given as 0.80c. Substituting these values into the formula, we can calculate the relative time:

Δt_relative = 90 / √(1 - (0.80c)²/c²)

Calculating this expression gives us a relative time of 37.5 minutes. Therefore, option a) 37.5 minutes is the correct answer.