NAME:

Quiz 1, Math 223, Section 2, 9-1-98

You are a park ranger in a dangerous mountain area. Late one afternoon, a group of hikers calls in on their cell phone: ``We're stuck up here. One of our friends broke his leg. I'm not quite sure where we are, since we left the trail a long time ago, but if you let the x-axis point to the east and the y-axis point north, then we're at a spot that looks like the graph of z = x² - y² if z is our elevation.'' The cell phone then dies, leaving you out of communication.

1.

On the topographic map of the area, label the location of the hikers with the letter A.

2.

The ranger station where you are is located at point B. Can you see the location of the hikers from the ranger station using high-powered binoculars? Why or why not? (Ignore the effect of trees.)

3.

There is a shallow lake with a small island in the center of it. Shade in the lake on the topographic map. Can the hikers see the lake?

4.

A stream flows from the highest peak on the map into the lake. At any given point along the stream, the water flows into the direction where it is steepest (and always toward lower elevation.) Sketch the path of the stream on the map. Will you have to cross the stream in order to reach the hikers in the shortest amount of time?