Question

A railroad curve is laid out on a circle. What radiusshould be

used if the track is to change direction by20o in a
distance of 100 miles? Round your answer to thenearest mile.

Answer 1

286.48 miles

Explanation:

The desired arc length is 100 miles and the desired change in direction is 20 degrees. The equation that describes arc length as a function of the radius is:

`Arc = (\theta)/(360)*2\pi r`

Applying the given values:

`100 = (20)/(360)*2\pi r\\r = (100*18)/(2\pi)\\r=286.48\ miles`

A radius of 286.48 miles should be used.