## April 15, 2010

### A Physics Problem on the Shanghai Middle School Exam

Supposedly one of the worst problems ever created.

Translation: 上海初中物理题 如此销魂！额滴个神！！！

Question:
A bear stumbled into a trap 19.617 meters deep. His falling time was only 2 seconds. What color was this bear?

A. White (polar bear)
B. Brown
C. Black
D. Black brown, Malay bear
E. Grey bear

Solution:
Using the classic equation s=gt2/2, it can easily be calculated that g = 9.8085 m/s2. Many people claim this is the acceleration due to gravity at the poles. They are wrong. g at North Pole is 9.832, which is much greater than our value on hand. Even at the equator, g is already 9.780.

I looked up the tabulated values and saw that this particular g corresponds to a latitude of 44o. There are no bears in the southern hemisphere. So, we know the location is 44o N.

The problem statement tells us that the bear fell into a trap and it was a trap large enough to contain him. On land, fewer animals are bigger than the bear. Thus, we can say with confidence that the trap was designed specifically for bears.

In addition, since the trap was on land, we can be sure that this was a terrestrial bear, who has bad vision and does not notice traps easily.

At this point, only B and C make sense.

To be able to create a 19.617 m hole, the soil must be soft enough.

Brown bears are typically located in regions of high elevations. They are ferocious, and the risks of hunting them are great. Furthermore, they are not as valuable, as bear paws and bile are extracted from black bears.

The places where the two types of bears live do not overlap. Thus, the answer should be C.