$3.(9$ points$)$ Consider a skyscraper built on the equator of the earth. The earth is rotating so that its angular velocity $\backslash (\backslash$omega $\backslash )$ is directed outward from the north pole $($i$.$e$.,$ the earth rotates west to east$).$ A person on top of the skyscraper drops a marble that falls to the ground. Ignore air resistance. The marble hits the ground offset horizontally from directly below the release point $($relative to the skyscraper$).$ In which $($compass$)$ direction is the marble offset, relative to the skyscraper? If you did this experiment with a skyscraper closer to the north pole, would the offset distance be larger, smaller, or unchanged, and why?