Practice Problems

Time Dilation:

Question 1:

Consider two twins 25 years old. One twin steps on a space ship (after studying physics in college) and travels through space at 0.95 c for 4 years according to her. How old is each twin when she returns?

Consider the muon described below for questions 2 through 4:

A muon is created in our upper atmosphere and travels toward the ground at 0.998 c. If it's lifetime is 2.2 x 10^-6 seconds.

Question 2:

What is the lifetime of the muon as observed by the earth's frame of reference?

Question 3:

How much distance would be covered by the earth as it sped toward the muon according to its own reference frame?

Question 4:

How much distance would the muon cover in our reference frame?

Consider Proxima Centuri for questions 5 - 8:

The nearest galaxy is Proxima Centuri and it is about 2 million light years from earth.

Question 5:

Without relativistic effects, how long would it take us to reach Proxima Centuri if we could travel at half the speed of light?

Question 6:

Without relativistic effects, how long would it take us to reach Proxima Centuri if we could travel the speed of light?

Question 7:

Considering relativistic effects, how long would it take us to reach Proxima Centuri if we traveled at 0.99 c?

Question 8:

How fast would we need to travel if we were to reach Proxima Centuri in 28 years?

Question 9:

Comedian Stephen Wright has a joke in one of his routines in which he is interviewing his boss to see if he would consider taking a job. He asks, "If you were in a car traveling at 99.999% the speed of light and you turned on your headlights, would you see anything?" Would you?