Chapter 39, Problem 39.72AP

A physics professor on the Earth gives an exam to her students, who are in a spacecraft traveling at speed v relative to the Earth. The moment the craft passes the professor, she signals the start of the exam. She wishes her students to have a time interval T₀ (spacecraft time) to complete the exam. Show that she should wait a time interval (Earth time) of

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

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