### Bear Accidents

Written by Barbara Williams

At the Albemarle zoo, animals are free to roam in a 5-square mile park. The visitors to the zoo are kept in cages or on trains well isolated from the animals that roam in their simulated natural habitats. Trains have been built on bridges over the open territories of roaming animals. Several sections of the rail system have been built on trestle bridges that cross man-made lakes through sections of the zoo occupied by the bear population. Unfortunately trestle bridges s hould not have been built over these sections because bears are good climbers and intensely curious. A bear playing in the lake below a trestle decided to climb atop the bridge. Shortly after the bear reached the top, a tourist train began to approach t he bridge. Startled by the vibrations of the track, the bear begins running on the rails. When the driver of the train sees the bear, the front of the train is as far away from the edge of the bridge as the bridge is long. The driver makes no attempt to change his speed because he assumes the bear will have enough time to escape onto the elevated land off the bridge.

As you work through the problem generate a list of learning issues.

1. What factors do you think should be considered in deciding whether the bear can survive or not. Include any assumptions the group thinks can be reasonably made.
2. Generate a list of different outcomes that are possible, assuming the bear remains on the track.
3. Select one of your outcomes. Make use of the old proverb, "A picture is worth a thousand words" and decide within your group the best way to represent graphically the action leading to your selected outcome.
4. Identify regions on your graph where the bear can survive, where there is a chance the bear might die. Explain your selections and describe how they differ.
5. How can the bear avoid a head-on collision? How can it avoid being run over from behind? (Provide qualitative and quantitative responses.) Are the conditions the same for both cases? Explain.
6. Did your solutions to the bear's dilemma depend on the factors you selected as relevant in question 1? Explain.
7. Is there any place on the bridge that the bear can be when first sighted by the driver so that no matter its running direction, the bear avoids a collision with the train? State any assumptions you make.
8. Assuming that there are bears of all ages in the zoo, and nearly all of the young ones are excellent climbers but slow runners, would you be comfortable employing this driver if the zoo officials wanted to maintain a stable bear population? Explain.

 "http://www.udel.edu/pbl/curric/phys201samp1.html" Last updated Nov. 22, 1996. Copyright Barbara Williams, Univ. of Delaware, 1996.