Amber ji, ...It's a good question ... It is related to understanding suborbital and orbital paths and hence very much related to ASAT and a satellite.
So, how will a ball going straight up fall 1 km away? Very confused...
But, I don’t think Amber ji is wrong that a ball thrown in an atmosphereless earth would land due west.
etc.. Let me make a few comments.
If interested please read carefully,
do not take my word for it or debate it for debate's sake do
check out any reputable sources if interested. To be fair, physics needed (and specially math involved) is not covered in Highschool or even UG physics/math courses. Generally one learns the full math treatment in Graduate level but this is fundamental stuff for ISRO or anyone interested in understanding ASAT or orbits.
(One good book, I liked was Goldstein's classical Mechanics)
To be clear, and remember we are neglecting effects due to air (As NRao pointed out earlier) 

In a sense, as we study in highschool (if ball being thrown on a cricket field) the ball thrown straight up falls back down in "your hand". A plane, flying , similarly behaves in a way, what normal high school physics courses teach us.
BUT this is so because we neglect complications as their effect is negligible at low velocities. In other words, an ordinary ball thrown straight up (even a ball regraded "fast" in cricket) will deflect so little (less than a millimeter) that it can't be measured and can be ignored. At around 200 m/s (which is fast but still a cannon can throw this fast).. the deflection is about a few meters, still hard to measure  ( presence of wind may have more effect)
but this fact is used by our armed forces in their calculations for artillery shells trajectories In fact, India's highspeed sniper rifles correct for this as it requires accuracy. At higher speeds things are even more counterintuitive.If you throw a ball faster than 11.2 Km/sec  The ball is NOT even going to return back to you. (Q: What will happen to it ? Think about it)
Similarly for planes (which are rather slow) one can ignore this "Coriolis force" .. but for missiles and ASAT type vehicles this effect is quite large.
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Here is some intuitive way to understand: When I talk about straight "up" there is generally no confusion between me and my neighbor. We don't have to worry about earth's roundness or spin.
This is not so if distances are large. "Up" in India is in different direction than "up" in USA.
This is what happens when we study motion of bodies under gravity on earth.
Another factor is, higher you go, value of "g" decreases. We can assume it is constant if we are talking about altitude of a few Km, but for sats the altitude is high and one has to take this into account.
And still another factor is:
The "rotating frame of reference" is not "inertial" and if you really have to understand ASAT type trajectories you need more physics/math than ordinary "ball" trajectories.
Hope this is helpful. For more, if interested, read up, there are plenty of good resources.