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 To (spaceship time) to complete the exam, show that she should wait a time (Earth Time) of
T = (To)sqrt[(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.)
Lorentz Transformations :
Time dilation: t=γt'
The Attempt at a Solution
Well I first I defined all the different times.
To= total time in the spaceship frame
t= total time in Earth's frame = γTo = To/sqrt(1-(v^2/c^2))
tx= time it takes the professor's light signal to travel from her to the students = x/c
T= how long the professor should wait to send the second light signal after the first one = t-tx
x is the distance between the professor and the spaceship when the students recieve the second signal.
I'm not really sure where to go from here. I know I've gotta use x'=γ(x-vt) where x' is the distance that the spaceship has travelled before recieving the second signal somewhere, but I'm not sure what time to use in it and stuff like that.
Any help would be appreciated.