Relativity - Professor in spaceship examning students

AI Thread Summary
A physics professor on Earth gives an exam to students in a spacecraft moving at speed v relative to Earth, starting the exam when the craft passes her. The students experience a proper time interval T_0, while the professor needs to determine the corresponding Earth time interval T before signaling them to stop. The solution involves time dilation, where T' is calculated as T' = T_0 / √(1 - v²/c²). The final Earth time T is derived as T = T_0√((1 - v/c) / (1 + v/c)), accounting for the light signal's travel time. This discussion highlights the application of relativity in synchronizing events between different frames of reference.
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And also check this one.

Homework Statement


A physics professor on the Earth gives an exam to her students.who are in the spacecraft traveling at a speed v relarive to the Earth.The moment the craft passes the professor,she signals to start of the exam.She wishes her students to have time interval T_0( spacecraft time)to complete the exam.Find the time interval T(Earth time) she should wait before sending a light signal telling them to stop.





The Attempt at a Solution


When in spacecraft T_0 for professor
T'=\frac{T_0}{\sqrt{1-\frac{v^2}{c^2}}}
T=T'-\frac{vT'}{c}=T_0\sqrt{\frac{1-v/c}{1+v/c}}
 
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seems alright by me, youv'e substracted the time it would take the signal to get to the spacecaraft from the overall time for the exam in the Earth's system.
nice work.
 
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