Ball Through Hole in Earth. Will it hit the side?

I'm not really qualified to answer, as my AP physics class never went over much rotational mechanics, but i think it would hit the side. The ball has some velocity tangent to the surface of the earth parallel with a tangent of the equator with magnitude 436m/s (2pir/86400), while the tunnel moving more slowly (proportional to height above center) closer to the center of the Earth, so I think it at some point hits the side. Don't trust me absolutely unless that stood on its own.