A ball is dropped from height \(h\) by someone standing still on the earth's equator.

(a) Does it fall to the east or west of a point just beneath the position from which it was dropped?

(b) When it strikes the ground, how far is the ball from the point originally directly beneath it, in terms of \(g, h\), and \(\omega\), earth's angular velocity? (Pretend there is no air resistance.)

(c) Explain the direction found in (a) using conservation of the ball's angular momentum in the inertial frame in which earth rotates toward the east.