## Contact

### Moscow

College of Science

Mines 321

875 Perimeter Drive MS 3025
Moscow, ID 83844-3025

Phone: (208) 885-6195

Fax: (208) 885-6904

Email: science@uidaho.edu

# Vandal Science News-February 2016

A Newsletter for Alumni and Friends February 2016

## Dean's Message

It’s remarkable to see both the variety and quality of research that goes on in the University of Idaho College of Science. Whether it’s work on modeling the evolution of viruses or on questions of adaptation to climate change, you’ll find the impact of UI researchers all across the scientific fields.

It’s wonderful to see many of our students take part in that inquiry and discovery. We really do provide the opportunity for a transformative educational experience here in the College of Science!

This issue features several stories that highlight why we’re so proud of our faculty and students. We hope you enjoy reading them.

– Dean Paul Joyce

## Vandal Science News Puzzler

This issue’s Puzzler is an aeronautical story problem with a geometric flavor:
A jet flies at a constant speed in a circular path over a city. At exactly noon it is observed flying due north directly above a park at the eastern edge of town. One minute later it is directly above a point exactly 3 miles north and 1 mile west of the park. How long will it take the plane to complete an entire circle?

## Solution

Consider the diagram at right. Because the plane was flying due north at noon, we know that the center of its circular path must be directly west of the park. We know two points along that circular path, and the arrangement helps us form a right triangle with sides R, R-1, and 3 (where R is the radius of the circle).
Using the Pythagorean Theorem:

(R-1)2 + 32 = R2
R2 - 2R + 10 = R2
10 = 2R

so R=5. But this means that the right triangle here is a 3-4-5 right triangle, so the angle inscribing the plane’s arc over that one minute time period is Arctan(3/4), or about 36.87 degrees. Now 360 divided by 36.87 is about 9.76, so it takes roughly 9.76 minutes for the plane to complete the entire circle.

### Correct Solvers

• Fred Burton (Mathematics, 1968)
• Carey Edwards (Forest Products, 2002; GIS Certificate, 2010)
• Gary Green (Mathematics, 1964)
• Tim Householder (Mathematics, 2002)
• Chris Marx (Biological Sciences Department)
• Leland Ogren (Chemistry, 1974)
• Greg Stenback (Geological Engineering, 1985; MS Statistics, 1987)
• John Stutz (MS Physics, 1973)
Diagram of the plane’s circular route.

## Contact

### Moscow

College of Science