October 2008
Problem of the Month
Centennial Problem
In his novel, Centennial, Mitchner describes the
cowboys traveling from Texas to Colorado. He states,
"A man standing on flat ground could see to a horizon 3.2 miles
distant. Astride a tall horse, he could see an additional
1.2 miles."
How much taller did the cowboy sit in the saddle than just standing?
Use 4,000 miles as the radius of the Earth.
Solution to the Problem:
The cowboy sits 6.019 feet taller in the saddle
or .001139993 miles or 72.23 inches taller.
Let x = man standing, and
let y = man on the horse.
Then y - x would equal how much taller he is in the saddle.
Since the line of sight to the horizon makes a right angle
with the radius drawn to that point on the horizon,
we can set up the Pythagorean Theorem:
