Chapter 1, Problem 31P

A physics professor on Earth gives an exam to her students who are on a spaceship traveling at speed v relative to Earth. The moment the ship passes the professor, she signals the start of the exam. If she wishes her students to have time T₀ (spaceship time) to complete the exam, show that she should wait a time (Earth time) of

$T=T_0\sqrt{\frac{1-v/c}{1+v/c}}$

before sending a light signal telling them to stop. (Hint: Remember that it takes some time for the second light signal to travel from the professor to the students.)