A pole-vaulter holds a 5.0 m pole. A barn has doors at both ends, 3.0 m apart. The pole-vaulter on the outside of the barn begins running toward one of the open doors, holding the pole level in the direction he is running. When passing through the barn, the pole just fits entirely within the barn all at once.
According to the pole-vaulter, which occurs first, the front end of the pole leaving the barn or the back end entering? Explain. What is the time interval between these two events according to the pole-vaulter?
t' = γ(t - ux/c2)
The Attempt at a Solution
Let S be reference frame of stationary observer
Let S' be reference frame of pole-vaulter
Subscript 1: Front end of pole leaving barn
Subscript 2: Back end of pole entering barn
From stationary observer's POV, back end of pole enters barn at the same time as front end of pole leaves barn. (Is this inference correct??)
t1 - t2 = 0
t2' - t1' = ... = γ[(t1 - t2) + 3u/c2]
Since t2' - t1' > 0, t1' occurs first. Therefore, front end of pole leaves barn first.
Is the calculation correct? Is there a more intuitive way of understanding which comes first?