I'm thinking what they're going for is that since d=(gt^2)/2 from rest, it implies that g=10 where ever this occured. This would then suggest one of the poles, hence white bear. However, last I heard g only varied up to 9.864 at the poles (from a twinge under 9.8 at the equator) so really the measurements must be somewhat off anyhow, probably more then enough to throw the thing out.
A 2 sec fall at the north pole should get you 19.728m, at the equator 19.5964, so in my mind the .1316 m difference isn't adequitly expressed as to make this a resonable problem. However, this is what I belive the aim it. Thus, correct the question and then accept my answer :-).
I've been looking (honestly not with amazing effort) for some experimental results for g over the world. I remember vaugely being taugh back in high school that g was a little over 9.82 (I was in Sweden at the time, perhaps 40 miles shy of the arctic circle) but that it'd be closer to 9.81 in more "normal" areas and even dip below 9.8 just a tad under the most extreme cases. If one considers only the theoretical, g=sqrt(GM/r^2) meaning it'd hit 10 around 6313.48 km from the center of the earth (GM assumed to be 398600.4418 ± 0.0008 km^3/s^2, error not large enough to affect 100ths of km unless I screwed that up somehow). This is a ways from the 6356 km at the poles unless there are 40 km dips around. However, I also recall someone mentioning that these assumptions don't hold true in real life for the classic thought experement of going deep inside the earth since it isn't uniform, the insides is heavier then the mantle and thus going deep into it one would be getting closer to the "heavy stuff" (increasing it's influence exponentially) while avoiding the influence of light stuff. Thus the somewhat paradoxal higher g at the poles, someone with limited knowledge of physics <raises hand> might assume that g would decrease as more mass is outside the sphere around the center which you are at, decreasing all the way to 0 at the very center (provided the mass tugging you outwards is uniform). I have no idea how the force from the other parts would pan out either really. However, it seems a little out there to think it'd go as far as g=10.
It's also a little hard to attribute any particular precision to the bear fall measurements. Assuming they are +-.5 (As the engineering part of me would assume from the context - 20 and 2, not 20.0 and 2.0. I'm being nice and assuming 20 is two value digits rather then (2 +-.5)*10^1) 18 2/9 >g>6.24 which would be pretty much anywhere. Considering the distance exact and the time +-.1 is still 11.08 to 9.07, not until +-.01 (pretty exact bear timing there) are we down to 10.1-9.9, which, baring a browbeating by experimental result from the poles, means it's whatever color you imagined it since it didn't happen or possibly whatever color is fashonable this season on worlds slightly denser and similarly sized populated by an intelligent space traveling race of past bears.