for part (a)
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rahuli think the ball wont deflect due to the coroilis force
(why should it there is no air resistence)
it gets deflected towards the east due to the coriolis force=2m*v* w
v=velocity of particle whose mass is m
w=angular velocity of particle
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i think the deflection will be observed for someone on the surface of earth just because the earth is rotating.
the time the ball takes to get downn earth rotates an angle Q
Q=length/radius
length here will be the deflection we will observe
i also feel that the acceleration due to gravity cannot be assumed to be g will have to integrate and get time in which it will fall down.
let the time in which it will fall be t
if angular velocity of earth is w
then the angle rotated in this time=w*t;
Q=l/r
l can be calculated
i you feel there is any problem in this approach plzzzzz reply