[UPSC CSE 2004] Rotating Frame (Q157, 20M)

For a freely falling body from the height h' on the surface of the earth in the northern hemisphere with a latitude \theta, show that the deviation of the body towards east at the final stage is given by \frac{1}{3} \omega \cos \theta \left(\frac{8h^3}{g}\right)^{1/2}, where \omega is the angular velocity of the earth and 'g' is the acceleration due to gravity.