Coriolis problem by conservation of angular momentum

A stone is dropped from a stationary helicopter 500 m above the ground at the equator. How far from the point vertically beneath the helicopter does it land and in what direction? You should solve this problem in two ways: a) by consideration of the angular momentum of the stone; b) by invoking the Coriolis force.

The b) part works out well in just a couple of lines, giving ca 24 cm to the west as an answer (correct). However, I don't seem to be able to get a) right. I tried to consider the stone as rotating around the Earth starting at a distance of R+500 m (R being the radius of the Earth) and then falling downwards with gravity and consequently speeding up in rotation as well, due to the distance to the centre of rotation getting smaller. After some nasty integrals this gave the answer to be 48 cm, about exactly a factor of 2 larger than in part b). However, I also had to use R in the final calculations which was not given in the question, hence this is probably not the way it was meant to be done.

Anybody who knows how part a) is to be attacked? Many thanks. :)