1. For any significant (kilometre scale) height, time of fall of a stone approximates to distance divided by terminal velocity. Let's say terminal velocity is 75m/s, and call the height 2 km. The fall will then take a little less than 30 seconds.

2. Assuming that the stone was not affected by any outside influence, in those 30 seconds, the Earth would have moved over 8 miles. Since nobody expects that result, something must have been missed.

3. In fact the stone was affected by something; it fell from a balloon that was stationary with respect to the surface i.e. also moving East at 1000 miles per hour. When the stone began to fall, it inherited that motion. On that basis, the stone would fall straight down.

4. However, to maintain its geosynchronous station, the balloon actually travels at a slightly greater speed that that of Earth, by reason of its altitude. The difference is 0.2m/s, assuming an equatorial orbit:

Earth 6371km*2*pi/24h or 463.3m/s

Balloon 6373km*2*pi/24h or 463.5m/s

0.2m/s through 30s is 6 metres. So, in this example, the stone would land some 6 metres further to the East.

5. Last but not least, the latitude of the balloon matters. If for example it was directly over a Pole,  the stone would again fall directly beneath the balloon.