November 2014
Problem of the Month

Ice Explorer Problem

When you take the Columbia Ice Field Ice Explorer (see picture below) in Jasper National Park, you go down a very steep hill.   At one point, it is 18 degrees.   What percent grade is that?

Solution to the Problem:

The answer is 32.5%.

To determine the percent grade, take the tangent of 18 degrees, which equals .3249 or 32.5%.

However, James Alarie wrote," I'm finding two different definition of road grade.   One says it is rise over run and a 45 degree hill would have a 100% grade. Another says it is vertical height difference divided by the length of road involved.

The rise-over-run definition would then use the tangent of the angle and the answer would be: tan(18)=0.3249 = 32.49%.

The height-per-road-length would use the sine of the angle and the answer would be: sin(18)=0.3060 = 30.60%."

Correctly solved by:

1. James Alarie	Flint, Michigan
2. Alex Houskeeper	Mountain View High School, Mountain View, Wyoming
3. Chad Fore	Gate City, Virginia
4. Braydon D Saxton	Mountain View High School, Mountain View, Wyoming
5. Keith Mealy	Cincinnati, Ohio
6. Chris Stringer	Mountain View High School, Mountain View, Wyoming
7. Dalton Hereford	Mountain View High School, Mountain View, Wyoming
8. Dane Covington	Mountain View High School, Mountain View, Wyoming
9. Ryan Woody	Mountain View High School, Mountain View, Wyoming
10. Austin Smith	Mountain View High School, Mountain View, Wyoming
11. Morgan Harris	Mountain View High School, Mountain View, Wyoming

Send any comments or questions to: David Pleacher