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!!!

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

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.


  1. i am regular visitor of your site and you are writing very nice so keep posting university admission

  2. It strikes me that Galileo would have thought that wherever on earth the bear fell it would have fallen at the same rate. Surely this is a physical problem , not a physics question? Maybe I'm just a historian who doesn't matter. Now if that bear had been wearing a feather fascinator, that could have fallen at a different rate altogether.

  3. I agree. This is a metaphysical problem. Actually you have a nice solution here. Do you know how you got graded?


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