A spaceship moves at 3/5 the speed of light relative to an observer.How long will each tick of a clock on the spaceship take,relative to an identical clock held by the observer?

Question

Quizplus · Accepted Answer

According to the theory of relativity, when an object is moving at a high velocity relative to an observer, time appears to pass more slowly for the moving object. This phenomenon is known as time dilation.

The formula for time dilation is:

t = t_0 / sqrt(1 - v^2/c^2)

where t is the time measured by the observer, t_0 is the time measured by the moving object, v is the velocity of the moving object, and c is the speed of light.

Plugging in the values given in the problem, we get:

t = t_0 / sqrt(1 - (3/5)^2)

t = t_0 / sqrt(1 - 9/25)

t = t_0 / sqrt(16/25)

t = t_0 / (4/5)

t = 5/4 * t_0

This means that each tick of the clock on the spaceship will take 5/4 as long as an identical clock held by the observer. Therefore, the best choice is C) 5/4 as long.

A Spaceship Moves at 3/5 the Speed of Light Relative