On our 45th Anniversary, Mrs. P and I rode one of the world's steepest Incline Railroads
at the Royal Gorge Bridge and Park in Canon City, Colorado. The length of the
incline is 1,550 feet and it is built at an angle of 45 degrees. The rate of descent
is 3 mph.
(1) How high was the starting point above the gorge?
(2) How many minutes did it take to reach the bottom?
Solution to the Problem:
The starting point is 1,096 feet above the gorge and it takes 5.87 minutes to reach the bottom.
To determine the depth of the gorge, note that the incline railway forms a 45-45-90 triangle. The hypotenuse
is 1,550 feet. To solve for one of the legs, you divide the hypotenuse by the square root of 2, which gives you 1,096 feet.
To find how fast the descent was, use dimensional analysis:
Click here for pictures from our visit to the Royal Gorge Incline Railway