A ball at a point on the earth with latitude \(\lambda\) is thrown vertically upward to a small altitude \(h\).

(a) Does the ball fall to the east or west of its starting point?

(b) Show that the ball strikes the ground a distance \((4 / 3) \Omega \cos \lambda(2 h / g)^{3 / 2}\) from its starting point.

(c) Explain qualiltatively the ball's path using conservation of angular momentum in the inertial frame in which the earth rotates eastward.