In the year 2100, an astronaut wears an antique, but accurate, "quartz" wristwatch on a journey at a speed of 2.0 × 10⁸ m/s. According to mission control in Houston, the trip lasts 14 hours. How long was the trip as measured on the watch?

Question

Quizplus · Accepted Answer

According to special relativity, time appears to slow down for an object in motion relative to a stationary observer. This effect is known as time dilation. The faster the object moves, the greater the time dilation.

In this case, the astronaut is moving at a very high speed of 2.0 × 10^18 m/s. As a result of this velocity, time appears to slow down for the astronaut, and the elapsed time during the journey will be less as measured by the watch compared to the time measured by the mission control.

To calculate the time dilation, we can use the equation:

T' = T / √(1 - v^2/c^2)

where T is the time measured by mission control, T' is the time measured by the watch, v is the velocity of the astronaut, and c is the speed of light.

Plugging in the values, we get:

T' = 14 hours / √(1 - (2.0 × 10^18 m/s)^2/(3.0 × 10^8 m/s)^2)
T' = 10.4 hours

Therefore, the trip lasted 10.4 hours as measured on the watch, which is the closest to option C (10.4 hr).

In the Year 2100, an Astronaut Wears an Antique, but Accurate