A pole vaulter holds a 16ft pole. A barn has doors at both ends, 10 ft apart. The pole-vaulter on the outside of the barn begins running toward one of the open barn doors, holding the pole in the level direction he's running. When passing through the barn, the pole fits entirely in the barn at once. According to the stationary observer in the barn, which occurs first, the front end of the pole leaving the barn first or the back end entering, and what is the time interval between these events?
I realize that the 'proper length' Lo = 16ft, and L = 10 ft. From there, I can get the velocity v and the factor y_v [measure of the departure of relativistic expectations].
I can then use the lorentz transformations, but I am having trouble finding the values
The Attempt at a Solution
L = (y_v)*Lo
10 = sqrt[1-(v^2/c^2)]*Lo
Solving for v: v = 0.78c
Thus, y_v = sqrt[1-(0.78^2)] = 0.626
Since we want to know t_2 - t_1, i used:
t_2 - t_1 = (y_v)*[(v/c^2)*(x'_2 - x'_1) + (t'_2 - t'_1)]
I dont know how to find the x primes and t primes (distances and times according to pole vaulter).