@keith yeah, it’s old as the hills. I remember back in high school I flipped the joke on its ear and had a bunch of kids thinking the physics teacher was teaching outdated junk. I ended up organizing a protest outside the front entrance before school one morning demanding that the poor guy be retrained in Darksucker Theory. Fortunately for me, the physics teacher had a sense of humor and thought it was hilarious.
@ken green You’ll be going light speed, both relative to the big ship and relative to a (relative to you) stationary observer. It is impossible to go faster than that within the confines of normal space. At near-light velocities, time slows down and space shrinks for the thing that’s traveling that fast. The ship you are “leaving” will appear to surround you. See the “Aberration in Action” section of this page.
Of course, if you actually hit the speed of light, you will also have infinite mass, be expending infinite energy, and time, for you, will freeze. So you’re basically both pretty amazing, and royally screwed if you try it.