A rocket of rest length L moves at v = c/5 relative to anobserver on the ground. A clock in the front of the ship (x' = 0)and the observer's clock (x=0) both read zero as the front of theship passes the observer. In the rocket's frame, a clock in thetail of the ship is sychronized with the one in the front. As thefront passes by (so t = 0), the observer fires a particle towardthe rear of the ship with ux = -c/5 relative to him.
a) According to the grounded observer, what does the clock inthe tail read as the front passes by? How long is the shipaccording to the observer?
b) What is the velocity of the particle as measured in the frameof the ship?
c) According to the observer, when is the fired particle alignedwith the rear of the ship?
d) Use the Lorentz transformation to get the coordinates of thisevent in the rocket's frame.
e) Show that, in the rocket's frame, the distance traveled bythe particle and it's velocity are consistent with the elapasedtime.